As I see it "African-American" is just another way to separate Blacks from this society and it's country. To a lesser extent you'll hear Mexican-American, or Asian-American, etc. Although admittedly, Mexican-American is more appropriate seeing as many Mexicans are true immigrants to this country.
All-in-all, when you put African, or European, or any other title before the "-American," it makes you seem less apart of this country than just the average American, born and bred.