Actually, we don't mind so much been called Americans or at least North Americans (no more than German or French mind much being referred to as Europeans). Well, franco-canadians from Québec don't give a damn about this anyway as our sense of cultural identity is as strong as the Americans' and we don't mind the association to the USA, but I do know some anglo-canadians who do get more irritated than us when called Americans - as to them it's perceived more as making nothing of the differences between their culture and the American one.

What a lot of Canadians and South-Americans mind a bit is that the term American became widely used in reference to citizens of the USA when it was the only country on the continent (the rest were colonies) and it never got changed when this no longer reflected reality and it became usual to refer to continental groups in geopolitics.

And thus you end up with people oddly minding to be called by their continent's name when it's proper to do it, and modern historians and some of the more "serious" media insisting to refer to Americans as "États-Uniens" (I don't know that an usual English alternative name for American beside "US citizen" exists - never heard it if it does - this may well be a Québec + South American thing only. French has another alternative way around it, as rather than use Americans/North-South-Americans in the continental context, we use an expression that in English would be "the people of the Americas" - weird sounding in English but not in French).