I disagree. I think she thinks her race is inferior and she is trying to make up the difference.
I have never bought that theory where an arrogant person is really suffering from a feeling of inferiority. I think it is what it looks like: Arrogance.
I think Michelle was raised on and thrived by hating and blaming whites. She has now found herself in a life that proves the opposite. So she is desperately clinging to that familiar crutch. She does not know how to let go of it. But make no mistake, part of that crutch theory is that blacks are better than whites.