Earlier quoted context omitted.
> Mayans and I are by now part of the greater western world "Western" is used as short-hand for the cultures "that have some origin or association with Europe. The term also applies beyond Europe to countries and cultures whose histories are strongly connected to Europe by immigration, colonization, or influence." Modern Mexican culture could be argued to be "Western". It would be difficult, on the other hand, to arg…
>> There is no ambiguity when someone says "I am American," as people from only one country identify themselves as such. Well, they have the right to do so when talking among themselves. When talking within an international audience, good manners suggest sticking to definitions that are internationally agreed upon. America is a continent, and US citizens are not more American than any Canadian, Argentinian or Peruvia…
[0]: https://en.wikipedia.org/wiki/Demonym
I'm aware that there are some continent categorizations that group North and South America as one continent called America, so one could use American to mean people who live in one of what are understood in other categorizations as North or South America. (Is that the continent categorization that you're familiar with? I just recently came across this, so if you wouldn't mind sharing where you learned this, and whether you're familiar with categorizations that count North America and South America separately, I'd be interested to hear more about it.)
That doesn't, however, mean that the usage of American to mean citizen of the US is wrong: it's very widely used in English worldwide. USian is assuredly not widely agreed upon as an alternative, at least in English which is the language of discourse here. Words have multiple meanings that need to be understood in context. Sometimes that context needs to be clarified.