Do black/African-American people care if they are called "a black person"?

I try to think about if I would care if I were called "a white person", and it doesn't bother me. However there seems to be this politically correct business where you MUST refer to such individuals as "African-American" and not "black". What do you think? I hate using the term... show more I try to think about if I would care if I were called "a white person", and it doesn't bother me. However there seems to be this politically correct business where you MUST refer to such individuals as "African-American" and not "black".

What do you think? I hate using the term "African-American" because I believe ALL citizens of the US are just that.... not some hybrid. Otherwise, then I'd have to be called English-Irish-Austrian-American, I was born in the U.S., but so were most blacks.

Thoughts?
Update: Just wanted to clarify that I am not trying to "label" anyone. It's just that it commonly comes up when trying to refer to or identify someone. It's an obvious feature that can be used to refer to or identify someone who would otherwise be non-descript.
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