Because he IS black.
As black as he is white. Apart from that he is black of African decent, not African American decent. Basically he has nothing to do with African Americans. Now before everybody jumps on me for saying black of African decent is something different than Black of Africa American decent, consider the following:
African Americans all have ancestors from West Africa, because that is where people in those days got their slaves from. The genetic variation in the black race in Africa is as big as the variation between the different races themselves. Therefore someone who has a father from Kenya is genetically very different from a West African person. As much as a white person differs from a West African person.
Culturally Obama was raised by white people, so he doesn't know more about the culture of black Americans than any other white person.
Before I am being accused of anything, I would like to point out that I am not a racist, in case any part of my post is being misinterpreted. I am merely pointing out that describing Barack Obama as "Black", in the sense of "African American" does not make much sense from a cultural or biological point of view.
Oh, and here is one more thing to ponder...... Black people in the United States are not 100% of African decent, because slave owners used to rape their female slaves. So over time, every black American, got a little bit of white genes in them. I mean after all, you won't find many "black" people in Africa as light skinned as Muhammed Ali or Kareem Abdul Jabber. (And yes, I picked their names on purpose)