Racism and Introspection

Racism (and sexism, etc.) is an objective phenomenon. It consists of actual harms to actual other people. That means introspection alone cannot produce an "innocent" verdict. For example, you can't decide whether supporting Chief Illiniwek is a good thing or not by thinking about whether you intend to honor Native Americans. You have to ask those Native Americans whether they actually feel honored.

Similarly, if you (as a white person, at least) bring out the standard "I'm not a racist" line, that pretty much means you are one. And I don't mean that just in the sense that everyone in our society is at least a little bit racist. If you think that you have the authority and ability to make a definite statement about your own racism, that implies that you think racism is wholly subjective, making the question about you rather than about the people of other races who are affected by your actions.

(This is not to say that introspection isn't incredibly important, or that white people should rely on people of other racism to teach us everything. But introspection alone is insufficient.)