I don't use the term, either. It seems more offensive to me than "black" does, not only because it assumes people are Americans, but also because most black Americans have no more to do with Africa than white Americans have to do with their country (or countries) of origin.
If you want to say "African American", you should also start calling people "Irish Americans", "Italian Americans", "German Americans", etc for white people. Almost no one does that, so there is no point to using the term "African American".
I also happen to know the term is offensive to people who do come from Africa and then become Americans, because I had a friend who did that. He thought the term was absolutely ridiculous given that most of the black people he'd met in America had never even been to Africa. So while the term "African American" accurately applied to him as an African who became an American, it did NOT apply to the millions of black people already in America.