Something occured to me earlier: how is "black" any different from "African American?"
Well, my kids don't much care for that phrase either, actually, but they prefer it over "black" because, well, they aren't and don't consider themselves to be "black." At least when someone calls them African American, the term is a bit broader and more nuanced. African Americans can be any number of combinations of races.
"Black" is just so either/or. You're either black or you're white. Except when you're both.
I don't guess we should resurrect the terms "mulatto," "quadroon," and "octoroon," - but at least they were more accurate!
Sometimes as a private joke between my oldest daughter and me, I will ask her (out of earshot of the kids, of course) "So, how are all the little quadroons doing today? And what about that little slanty eyed devil you've recently acquired?" (Her adopted Korean son!)
So you can see that our family doesn't take offense too easily at this sort of thing. Heck, my dad calls my two sons in law "Mordechai" and "Ali Baba" (one is part Jewish and the other is not a drop of Arab, but he's part Sicilian, looks Arabic and his stepfather is Muslim - hence the Arabic nickname!).
So - we're not a very politically correct family but in a family that looks like a UN delegation, we may as well have a sense of humor about these things!
People of mixed racial heritage often don't like the feeling of being pidgeon holed or forced to identify with one race OR the other - when they are proud of their complete racial heritage.