Yes, I'm well aware that Ireland is not in Great Britain. That does not change the point that many people in the US (who are of course not Ireland's colonizers)

Yes, I'm well aware that Ireland is not in Great Britain. That does not change the point that many people in the US (who are of course not Ireland's colonizers) use Britain to refer to the UK as a whole. No one in the US would say "I'm going to Belfast, it'll be nice to hang out in Britain." It's shorthand for referring to the state. As in, "Britain has a new PM."