You will never reverse this oddity of English vocabulary, no matter how much you bellyache about it on the Internet. Sorry that basic lingual fact contradicts your sense of fairness or whatever.

If it helps, you can think of "American" as shorthand for "American of the United States". If that doesn't help, I suggest you just get over it.

Nobody from Canada or Mexico would say they are "an American." Americans are residents/citizens of the USA.

Not totally true. I went to school with a lot of Mexicans and they would get verbally upset when I referred to the US as "America". As a Canadian, I could care less but they were very adamant about it.

I feel bad for people from Tijuana, as they are Californian and American but reside in neither California nor America.

The titles come from culturally distinct regions.

For the most part they say "North American," South American or "Latin American" even "Anglo Saxon America" for North America not including Mexico, go figure.