Social psychologists have devised a genuis way to measure our implicit biases; that is, they have found a way to tap into those biases that we hold unconsciously and/or know better than to reveal in mixed company. You can learn all about it and take all kinds of tests to reveal your own biases here.
One thing these investigations have revealed is that many of us internalize biases against the groups we belong to. So, women can be sexist and people of color can be racist. Even if people consciously reject these biases, they often sink in anyway and lead to a kind of self-dislike.
Someone sent in a postcard to PostSecret this week that illustrates just this phenomenon: