Is "African American" a weird/unfitting label? (Description has details)

I get that it's an acceptable label, and I don't get bothered when people refer to me as such (considering I'm black), but I don't see it as fitting. For example, if someone says Asian American, you usually think of an Asia-born American, right? So to me, the real African Americans would be the people who came from Africa during their lifetime, and are now Americans. I don't mean to say that it makes anyone more or less American, but African-born and American-born black people have separated into two different cultures and sometimes even have very different facial features. And from what I've heard (from Africa-born Americans) some of them don't agree with the term either. Hope this makes sense. And I don't mean to offend if I have... What do y'all think?

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