In response to comparison of the term African-American
instead of nation
-specific) with Irish-American or Mexican-American (nation-specific): We must remember, dearest beloveds, that our American siblings descendent from African slaves have not the advantage of knowing just where in Africa their ancestors were kidnapped from.
The U.S. has the distinction of being the only nation that systematically broke down the family and cultural structure of Africans enslaved. African slaves who attempted to teach their children native language, religion, custom, and history were routinely punished for doing so(ranging from a "good-talking-to" to having family members sold off).
It is a basic human psychological need to identify with your "roots," and only those deprived know how damaging is this deprivation.
What term is politically correct? I don't know. But, I suspect an underlying love and respect for one's fellow man supercedes terminology. The best answer to the "which is correct" question I've heard yet was when my former coworker Alex, (a black man) was asked, "What do you prefer to be called?" he replied, "Oh, I like 'Alex.'"