First exxplanation is that is it because his skin does relect that of a black person. If so, then this is is merely the result from a case-to-case analysis.
But I doubt that is the reason. Alternatively, he is considered black only because his father is black? This would be analogous to the custom we have back in China about 30 or so years ago - one's 籍贯only follows that of his father. In other words, Obama would not be considered as black if his parents' race reverse (i.e., his father being white and his mother being black). However, although this theory would be more systemic and generalized than the first one, I feel it is no more plausible than the first.
Then we came to the third one which is a more likely and profound explanation. That is, unless you are pure white blood (eve if 75% white), you will be considered non-white, but instead classified as a minority according to the dominant non-white genetic trait you have. Assuming this is indeed the norm of the social conception about people with mixed racial traits, what does it tell us?