Why do we refer to ourselves as Americans?

So -- I understand the objections to the practice of referring to U.S. citizens as Americans and the United States as America. I also feel like it's no big deal, since it's just an established practice and more of a crime of verbal inspecificity than pure chauvinism.

One significantly mitigating factor in this usage, though, which doesn't receive that much attention, is that there isn't an easy way to refer to the state of being a U.S. citizen. What do you use in place of American in the sentence, "He's American"?

Actually -- it occurs to me extemporaneously that there are probably folks out there promoting alternatives. Usian or something. (Although in that, you have the immediate sense that the phrasing contains the assumption that everyone else is Themian, which seems at least as problematic as the assumption that the U.S. = the American continent.)

Maybe I'll have to look into what's out there. I bet there are some good ideas -- and some really ridiculous ones.