Why is the politically correct term African American?

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Why is it so offensive to call someone "black" instead of African American? I don't go around saying that I am European-American, or Italian-American, why is this? I mean not all black people are of African decent, some are from Jamaica or Dominican Republic. I don't even hear people say "caucasian" when referring to us, even if they are black themselves, so why do we have to avoid offending by saying "African American"? Just curious.