I'm one of those you are describing. Albeit, it doesn't offend me. It confuses me.

If I had to put myself into everybody's shoes, I would then say that first, our disagreement on how to name continents is a matter of culture. Yes, we say America is a continent, and you say it is North and South America. Normally I would argue that for it to be a continent, it needs to be one landmass. Which works in favour for me. But then, we would have to acknowledge that America and Asia is interconnected, and also, we do not say Eurasia; we say it is two continents, Europe and Asia. Which has defeated me once again.

So I don't really mind the continent part.

It is also true that not ever would a Canadian or Brazilian call themselves American. But do they call themselves North American or South American? I'm honestly asking, because I do not know. My guess is 'yes'?

It doesn't matter, if I look it through your or my eyes, it seems an annoying matter. Because Europeans and Americans have had a very different education about it. The fact that you call yourselves American is very descriptive and straight to the point. For us it seems egotistical, like a disregard to your fellow neighbours who share a continent with you.

My conclusion is that we Europeans are too annoying about it. Instead of accepting two different viewpoints, we somehow try and force our idea because we think it is "right". But I think we can rest and say that it is just a matter of opinion, education and therefore not really up for debate.