Look, this is why silly liberals like me say things like "race is a social construct." That isn't to say there aren't some persistent genetic differences between populations, but those populations don't match up very well with what we, as a society, call "race." And, those conceptions of "race" differ quite a bit from country to country.
But, as for why this issue is coming up now specifically, Obama himself says it much better than I ever could:
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If I was arrested for armed robbery and my mug shot was on the television screen, people wouldn't be debating if I was African-American or not. I'd be a black man going to jail. Now if that's true when bad things are happening, there's no reason why I shouldn't be proud of being a black man when good things are happening, too.
I've never been a big fan of the term "African-American" as it ties a race into a geography, and it becomes increasingly confusing as immigration patterns become more complex. I'm happy to identify people in any way they want to be identified, but I do think the adoption of the term has been counterproductive in a number of ways. Is Theresa Heinz Kerry an African-American? Would an Afrikaaner immigrant to the US be? What do we call black Hatian immigrants, or black citizens of Britain? Once it becomes complicated, we default to the term which is really the primary issue - skin tone.