Why do British people who want to abolish the monarchy act like this?

[boltj]

I know that there are a lot of people in Britain who want to abolish the monarchy for various reasons whether it be due to them thinking that the monarchy is scandalous, a waste of money, a symbol of inequality, anachronistic etc. however, why do I rarely hear British people who want to abolish the monarchy claim that abolishing the monarchy will prove that Britain is independent in the same way that Australians who want to abolish the monarchy often do?

Australia and Britain both share King Charles and some Australian republicans say he is a foreign head of state, “not one of us” and that by abolishing the monarchy, Australia will prove to the world it is distinct and independent so why don’t British republicans employ similar rhetoric instead of just harping on about inequality or cost?

Calling NI part of Britain is incorrect. It is part of the UK.

The term British Isles is also contentious. The term used in official documents/joint agreements between Ireland and the UK is "these islands". You can also use The Atlantic Archipelago or The United Kingdom and Ireland.

I think it’s a messy edge case, but it’s too doctrinaire to say “Britain” is never and can never be short for “the British Isles” the geographical term and must only and always be short for “Great Britain” the political one.

Is Canada “part of America”?

Is England “part of Europe”?

I don’t think being contentious politically comes into it (is someone who says they are from Derry City incorrect? Is someone who says they are from Londonderry incorrect? Neither is incorrect just becuase it’s contentious).

Your Canada/England' examples are not equivalent. You could refer to a Canadian as American or an English person as European as they are from those continents. However, referring to the Atlantic archipelago as Britain would be equivalent to calling the American continent Canada or calling Europe England.

So no, Britain is not, and cannot be, short for the British Isles.