You know, I've read this, and I've certainly experienced it, but every time I see it happening it amazes me. People really do only see their own disadvantages; privileges are hard to see. Of course this makes sense, you see what keeps you down and we don't like to acknowledge that we have had boosts along the way. But often, when those barriers act in very similar ways, it's fascinating to me how someone can acknowledge one kind of inequality but categorically deny that another exists.
For example, I was talking to someone yesterday; at first, he didn't want to believe that there was any inequality in the world. He, of working class background, was relatively quickly able to see his class disadvantage, but adamantly did not want to see inequality or believe that coming from a non-white background might hurt ones' chances to achieve the "American Dream." We won't even get into gender.
This is fascinating: we were talking about unions, and how raising the minimum wage and increasing unionization might reduce some of the pull factors that bring undocumented immigrants to be exploited by corporations who know that they can hire them cheaply. He agreed and was all for unionization. Then we were watching CNN and a union leader from the NY transit authority started speaking. He had an accent and may be an immigrant; most of the audience for the speech were people of color. Suddenly, they were "trying to make the white man give them more," not fighting for, you know, better wages or working conditions. He literally, because of the ethnicity and race of these people, was not able to see the disadvantages that he had no problem imagining when the disadvantaged people were (in his head) white.
I guess being able to ignore white privilege is a privilege in itself.