Edit: Following feedback, there will now be a part 2 to this post which will be the more offensive case against them. This first part is more of a defense against the pro-monarch claims.
Before I begin presenting the case, it's important I make a couple of points clear. The reasons I'm about to post aren't what caused me to take a republican stance they merely support the position. The reason I oppose the monarchy is simply that hereditary power and wealth by birth right to a single family is abhorrent to every sensibility I have. The reasons I will include here are primarily arguments against the monarchist position from a British perspective. Finally, whilst I may not quote www.republic.org.uk often, my early education in the subject was informed from that site so many of the arguments could probably be found in a similar form somewhere on that site, therefore it seems only fair I credit them (though I don't entirely agree with all their positions either).
The Tourism Argument
The Claim
One of the most often repeated claims of the benefits of having a British monarchy is that they bring in tourist cash. Were we to get rid of the monarchy the cost to the british tourist industry would be huge.
Response
Really, this claim should be dismissed without any evidence to the contrary. Even if it were true, is "well foreign people think it's kinda funny" a good way to decide on the head of state? Or maybe decisions of who gets to be the head of state should be made on which option gets most money from tourists? These are obvious preposterous positions. Fortunately, they're also based on a complete falsehood.
The Association of Leading Visitor Attractions tracks the number of tourists visiting attractions over time. Their figures for 2012 show (after enough scrolling) that not only do the royals not play a particularly big role in tourism, it might actually be better if they vacated their properties permanently such that we could open them as museums In case you had any concerns of the potential bias in the figures, the president of ALVA is the Duke of York.
The Finances Argument
The Claim
In a similar way to the tourist argument, this claim is that the royals bring in such an income to the country that it could lost billions in lost revenue if we no longer had them. Fortunately many monarchists even wouldn't go that far and simply assert that they don't cost much and perhaps even result in a slight income.
Response
This claim should really be considered as absurd as the tourist one in terms of the pure 'money' argument in that it's absurd to make a decision about who should be head of state on the idea that we might make a bit of cash. As it is the cost of the monarchy has increased almost every year for at least the past 20 years. The civil list cost has officially been locked since 2001 at £7.9million (source) and yet we find that the cost has increased every year between 1991 and 200 until it dropped mildly in 2009 following a £2 million rise the year before (source). They managed to rally themselves though for 2010, dropping again in 2011 by £700,000 to a mere £13.5 million according to the official royal finances. With all this money over the £7.9m though, are they funding themselves?
..no, of course not. The lock on the civil list came after 10 years of huge over payments and the money is taken from the 'civil list reserve' to make up the difference, which is to say the money they didn't need to spend in the 90s (source).
But in 2011 the civil list reserve was running out, so rather than maintaining the "freeze" of finances which had resulted in more money every year a new system has been installed known as the sovereign grant. This grant gives the Queen 15% of the crown estates net revenue which even according to conservative sources bemoaning it isn't more is an increase of £5 million for this year.
But wait, there's more! When you take a lot of the costs in to account we get the official cost of the royals at 62p per head in 2010 (source). This number has obviously increased, but since I can't find more recent data we'll stick with 62p for now. It's important to notice that the official figures refuse to include security which is likely another £100m according to even pro monarch papers in the Briain (source).
The estimated costs in total end up being around £202million in 2010 (source) which makes it roughly 100 times more expensive to maintain than the salary of the Irish president (source) for example. Maintaining an entire family of wealthy elite isn't cheap, and it certainly doesn't bring money in to the country.
The Stability Argument
The Claim
Many of the most developed countries in the world have monarchies. Indeed, many of the most stable in the world too. Without a monarchy, we would lose that stability.
Response
To this claim there is the obvious retort that many countries, including the US, are able to be stable and developed without a monarchy, and the fact that many monarchs around the world are anything but (for example, Saudi Arabia and Thailand). The point is that, it's more likely that stable countries keep their monarchs than that monarchs produce stable countries, not least because of the examples throughout history of countries after the removal of monarchs. Britain won't fall apart if the Windsors are removed from power.
The "They Don't Really Do Anything" Argument
The Claim
They're relatively benign, and they don't really do anything or cause any harm so we don't really have any reason to get rid of them.
Response
It is certainly true that the current monarch doesn't really do that much, but that's no reason at all to leave an unaccountable, unelected head of state. Especially when that unaccountable head of state provides all the authority for parliament. Even more so when that power includes a royal veto which is still used and which has been offered 39 times (source).
On top of that, we're still left with the position of a head of state which is not only undemocratic, but is also the very definition of anti-democratic nepotism!
The Crown Estates Argument
The Claim
This claim typically refers to the idea that taking the lands (and the revenues they generate) from the monarchy is either wrong and/or will be an expensive and protracted process. Sometimes this also includes the idea that taking their property and wealth in general has similar problems.
Response
So, my response to this might be a bit coarse, as it'd be 'why not?'. They've leeched from us for long enough and been well compensated, there's no reason at all the country shouldn't just sieze their stuff and kick them out of their homes and let them live like everyone else. I appreciate though that not everyone is going to share that view, so I'll include a more reasonable reply which is more typical of a republican position.
So in a less terse response, the most important point that needs to be made is that the royal estates are not the property of the queen, and certainly not of the Windsor family. The crown estate was established for the state at a time when the monarch actually funded the affairs of state. At the time this was exchanged from one state branch to another (the government) the funding of the state passed over aswell. This estate belongs to the British state, not to the monarch and absolutely not to one family. The fact that they're now getting 15% of the income from it in a move of political spin from the 'benign' palace shows simply how important it is to get rid of them. There is literally no claim to be made by the Windsor family to the money, so it is in no way theft to not give them all that land and property when they leave.
Now, I wouldn't expect you to take my word for it so how about we use the explanation by the Crown Estate itself to judge:
The Crown Estate belongs to the reigning monarch 'in right of The Crown', that is, it is owned by the monarch for the duration of their reign, by virtue of their accession to the throne. But it is not the private property of the monarch - it cannot be sold by the monarch, nor do revenues from it belong to the monarch.
The Government also does not own The Crown Estate. It is managed by an independent organisation - established by statute - headed by a Board (also known as The Crown Estate Commissioners), and the surplus revenue from the estate is paid each year to the Treasury for the benefit of all UK taxpayers.
To explain further, one analogy that could be used is that The Crown Estate is the property equivalent of the Crown jewels - part of the national heritage and held by Her Majesty The Queen as sovereign, but not available for her private use.
The Government also does not own The Crown Estate. It is managed by an independent organisation - established by statute - headed by a Board (also known as The Crown Estate Commissioners), and the surplus revenue from the estate is paid each year to the Treasury for the benefit of all UK taxpayers.
To explain further, one analogy that could be used is that The Crown Estate is the property equivalent of the Crown jewels - part of the national heritage and held by Her Majesty The Queen as sovereign, but not available for her private use.
-source
This position is affirmed elsewhere on the site with the explicit statement that "No, this [claim that the estate is the queen's property] is misleading." Getting rid of the monarch merely means the Crown Estate continues paying its income to the treasury, and the Windors lose nothing - by virtue of never having it. And yes, that also means the crown jewels belong to the people of Britain, and not the Windsors.
It's also worth noting therefore that the myth that this income makes up for the cost of the monarch and should be considered as a surplus to the taxpayer on behalf of having a monarchy, it outright shattered. It's unsurprisingly believed by some people since Charles especially has spent the past 20 years trying to convince the public otherwise (source), but it is an outright fabrication and a money grab.
Unfortunately though, this claim is far from done. Were I to leave it here, the claims 'What of the duchies!?' would inevitably follow from the more informed monarchists on the site who I imagine would never let me get away so easily. Fortunately I can refer to The Official Site of the British Monarchy which explains with regard to Cornwall at least:
Under the 1337 charter, as confirmed by subsequent legislation, The Prince of Wales does not own the Duchy's capital assets, and is not entitled to the proceeds or profit on their sale, and only receives the annual income which they generate (which is voluntarily subject to income tax).
He is in effect a trustee, and is not entitled to the proceeds of disposals of assets. The Prince must pass on the estate intact, so that it continues to provide an income from its assets for future Dukes of Cornwall.
It's also worth noting that in court the Duchy has also been recognised as a public body. (Source).
There is no legitimate claim by the Windsor's to any of these lands, except those few homes which belong to their personal private estates. The crown lands belong to the state, as they always have, and there would be no theft of property needed to remove them from their current position.
The International Diplomacy Argument
The Claim
According to this claim, the work that the royals put in to international diplomacy is invaluable, securing trade and diplomatic ties.
Response
The first and most obvious point to bring up here is that the vast majority of diplomatic work is done, unsurprisingly, by trained diplomats. Especially unsurprising since the queen actually appoints diplomats to do that work (there were around 2000 diplomats last year -source). Between 1952 and May 2011 the Queen has undertaken 108 state visits (source). That's less than 2 a year! She must be rushed off her feet with all this diplomacy; being given gifts, seeing children dance and shaking people's hands once or twice a year.
Of course though, it isn't just the Queen. According to the official monarch website they do perform 2000 "official engagements" a year total for everything (diplomatic or otherwise, including all UK events) when you take the whole royal family in to account . They're pretty good at partying though, with 70,000 guests a year attending their parties. (Sources).
In addition to their lack of diplomatic work, the work they do actually do could quite easily be done by other people without any particular worry. The head of the state being sent to give a readied and choreographed talk and meeting is going to be regarded as highly whoever that head of state is, provided they don't screw it up (say, by dressing up as a nazi [source] or being generally offensive... [source]) or anything. Can you image the complaints if this claim were true "Oh, the US is only sending their president to shake hands, not a monarch. Obviously they don't care about diplomacy"?
The idea that a royal family is needed for diplomacy is kinda silly, and we're all fortunate they don't do much of it.
The Tradition Argument
The Claim
Britain has traditionally been a monarchy and it would be a great heritage loss. This claim sometimes includes the loss of traditional ceremony associated with the monarchy.
Response
Even at the best of time "it's tradition!" is a bad reason to keep doing something. There's also no reason to chuck out all the traditional ceremony of the guard or the head of state sending letters to people. It's actually hard to think of anything important that would be lost in terms of "tradition", and it's certainly not a reason to keep an undemocratic system in place.
The Hard Working/Charitable Argument
The Claim
Somewhat tied to the diplomats claim, the royals are said to be very hard working individuals. They have hundreds of appointments a year, and also raise considerable money for charity.
Response
Ideally I'd just quote former deputy private secretary to the prince of Wales, Mark Bolland from the documentary "Janet Saves the Monarchy":
"the Windsors are very good at working three days a week, five months of a year and making it look as though they work hard"
and with the sources from the diplomat question be done with this one, but for the sake of completion I'll keep to the same standard as other questions.
So, first, if we're going to judge who should be head of state by how hard someone works, then probably most politicians and certainly every manual labourer in the country is a better choice than any of the royal family. Presumably though, the argument goes that the monarch are also hard working, so deserve their unquestioned, hereditary and anti-democratic position at the top of class society. It's worth noting that an alternative without the baggage would be quite capable (and expected) to work hard.
As I have already somewhat shown though, the work of the royal family on the whole is minimal and even by their own most exaggerated definition, catch all of anything they did definition used by their own sources, at best the entire royal family contributes 5 undefined engagements a day to the UK, which do include parties and attending dinners. Not exactly what I'd call hard working.
As to the charity claim it is true that, of the millions of pounds they're unduly given on behalf of the British tax payers to a single family rather than to helping they people of Britain, they do give some to charity. But what of the work they do? Well, even their own website struggles to come up with anything but lending their name and celebrity status to a charity - something we hardly need the monarchy for.
The Trained From Birth Argument
The Claim
The monarch has been trained from birth to be the head of state and so is the best trained for the job.
Response
I need to start this response with a quick preface. Fortunately, in my experience, this is a position that most monarchists don't actually hold. I wouldn't have even brought it up here if it wasn't used as a reason earlier in this thread and I hadn't heard it before as I think it would have been unfair to suggest this is a common argument of the opposition. It's not a common reason and I'm not trying to strawman the majority of the opposition who will generally attempt more sensible issues, like the others I've addressed in these posts.
Ok, so...yeah. First, and most obviously, we could train anyone from birth to be the head of state if that's really what you value as a job qualification (Britain's Next Tot Monarch?). The idea that someone must be trained from birth, or that it's somehow advantageous is laughable, especially when you consider how many people have been trained for jobs since they were old enough to understand the concept and do remarkably well. For examples see every single other job on the planet. Inventors and decent politicians for instance don't need to be trained from birth to fill the role. Many other countries in fact do quite well with a head of state who is someone who has actually been judged to be a good fit for the position, rather than just hoping that telling them from birth to be good at it is sufficient. There is no other job in the world this argument would be accepted for, it is utterly ridiculous.
And of course, you still have to explain Philip.
The President Blair/Cameron Argument
The Claim
If we get rid of the monarchy we'll have a US style president who runs the country and it'll be political and short sighted. A neutral monarch who doesn't have to worry about being held accountable at elections can focus on being the head of state to a far greater capacity than an elected president.
Response
There is no reason (nor suggestion that I'm aware of) that the replacement head of state need be a political figure. We already have the speaker of the house as a neutral political figure, there is no reason at all that we shouldn't be able to establish something similar. Additionally there's no reason that the president needs to be head of parliament or to expand the powers of the head of state beyond a ceremonial role, ensuring that parliament acts only within constitutional boundaries and representing the UK when necessary.
The 'Popular' Argument
The Claim
The majority of people like the Queen and/or the monarchy so they should be kept in place. This claim also exists as 97% (I may be slightly off on the number, I can't actually find a source for it) of people voted for pro-monarch parties in the last general election.
Response
The second part of the claim is less common (but I did hear it yesterday from a senior member of the BritishMonarchSociety) but far easier to deal with so I'll start there and then move on to the more comon, and more sensible variant. The fact that most people in the last general election voted for one of a small number of candidates standing who had a chance to win is not representative of the number of people who support the monarch. Pro-republican numbers always poll significantly higher than 3%, it is simply the case that there is currently no alternative to vote for, save for the Green Party in this regard.
As to the majority supporting the monarch, it's worth noting that it depends significantly on where you ask and which question. Support for the monarch is highest amongst the elderly, where it reaches up to 88% according to the most pro-monarch trending recent poll I could find and that poll shows that overall 13% support a republic and 7% presumably didn't mind. At first glance then, it does look like this claim has merit, but there is more to be mentioned.
First, that poll is taken with the context of the royal baby, and support traditionally rises everytime we have one of these affairs or another. There are also vast differences across the UK in their support of the monarchy, when the older generation is unfortunately no longer with us, and especially with Charles who is almost a case for a republic in his own right, those numbers will drop. The support in Scotland is traditionally lower also.
Second though, the list of claims I have shown alone will show that most people's support is based on an long term misinformation campaign which has even managed to convince people that the monarchy doesn't cost money (or costs very little) which is demonstrably false already, but would be significantly clearer had the monarch not demanded the right to immunity from the freedom of information act and immunity to real accounting such as security costs, event costs and the public lands which are used to fund them which would massively increase the cost. The fact that so many of these claims are believed, it's no wonder they have support; they're money printing masters of diplomacy who are loved by all and far better than any politician to believe these claims!
It's also worth noting though, that this post is illegal under British law. No, seriously, I'm not allowed to advocate for the replacement of my head of state - it is illegal under several acts of treason which still apply today which apply a life sentence. It wasn't until 2003 that it was finally judged to be in breach of the human rights act to punish peaceful means of protestation, though the law still remains should that act be repealed - something which is advocated by senior members of the current government! This case had to be brought by one of the largest newspapers in the UK because they had wanted to advocate for a republic, is it any wonder there is so little widespread opposition? Anything which causes alarm to the sovereign is still punishable by life in prison, though fortunately not death as it would have just 15 years ago.
The Ceremonial Argument
The Claim
The role of the monachy is basically just ceremonial and so there is no reason to remove them.
Response
The ceremonial only role of the monarchy is overstated, and often refers to little more than their laziness, covered earlier. To describe the royal family as still ceremonial is to ignore the real impacts they do have. For instance, as I write this I am 'a subject of her majesty', replace 'her majesty' with 'President Obama' or whoever your personal head of state is if you fail to see why that's offensive. The princess story may seem quaint to the outsider, but perhaps not so much as a reality.
It's also worth noting, you're considered owing duty to the crown (and so liable for treason) if you have a British passport, so there is yet another case where the monarchy isn't just for show - I am forced to be labeled a traitor if I wish to leave the country legally for any reason. I become liable for treason laws if I dislike the monarchy by having a British passport, because it is issued in the monarchs 'protection'.
As I have already mentioned in the 'They Don't Really Do Anything' section, they also have a dangerous veto which they can use against any law they feel will imapact them. Privy Council exists as a mechanism to get around parliamentary scrutiny, which one member resigned from citing it was being used in a way which "borders on conspiracy". This council is of course in addition to the weekly visits in which the Queen is consulted by the Prime Minister on legislation whereby she may warn him against proposals. We will, of course, never know which legislation has been warned against.
In addition, the monarch still holds the power to choose a Prime Minister or to dissovle parliament. These are real things she can elect to do. 'But she'll never use those powers!' will come a chorus no doubt, as if leaving such power as a ceremonial role to never be used were in any way a sensible course of affairs.