Well, technically, Obama has more right to call himself an African-American than almost every black person in America. Being as how his father was an African (Kenyan, to be exact) and his mother was an American. I think the term "African-American" is bullshit. There are a lot of countries within the confines of Africa. The countries of northern Africa are mostly Arabic. You don't see Algerians claiming to be African anything...yet, technically they are. White people don't get offended when somebody calls them white. Why would it be offensive to call a a black person black?
A funny thing that I have noticed is that every first generation black African person I have ever met doesn't like American blacks. These people, like most immigrants, are tireless workers who feel immensely blessed to have the opportunity to come here and pursue the American dream.