Another way that racism harms white people is by denying them the ability to develop their critical thinking. This is due in part to the constant, regular reinforcement that white is right. White people are raised in an environment in which they are regularly assured of their superiority. Their experts are white, like them. And they often live in segregation, thus denying them the opportunity to be exposed to other viewpoints.
What happens in a culture of white supremacy? White people assume that they are the experts. Even in the absence of any history, education or knowledge.
The most blatant example of this is when a white person (typically a white man) is pontificating about a subject and is challenged when a person of color expresses an opinion. The white person will assume that the person of color knows nothing about the subject and will strive to “correct” him or her. I’ve had this happen when a white person who was not in my field was speaking with authority about something in my field. They never assume that you might actually be knowledgeable on the subject, nor do they assume that you might have professional credentials. (I’d also note that this is a very common experience on the part of people of color. And I recently heard a anecdote about this happening to a writer of color with a white man who was discussing her book. Only he didn’t know she had written it.)
It does not cross their minds. This is racism.
It does not even cross their minds that they are noticing race; this assessment occurs unconsciously.