Suppose you are a white student at an elite college or law school in an America without affirmative action in admissions. You observe that although there are not very many black students in the school, the ones that are there are about as smart as you and your fellow white students, that being why they, like you, got in. You may notice that blacks other than your fellow students are mostly not as smart as you are but that is true of whites as well. So far as your own direct experience is concerned, you have no reason to believe that whites are smarter than blacks.
Suppose you are a white student at an elite college or law school in an America with affirmative action in admissions. A few of your black fellow students are about as smart as you are — the ones who would have gotten in without affirmative action — but most are not. If you are at a school one step down from Harvard or Stanford there will be few if any black students as able as the average white student at your school because students that good were accepted by a better school. On the basis of your experience of the fellow students you interact with you conclude, even if you are careful not to say, that blacks are less intelligent than whites.
Hence one effect of affirmative action is to increase racial prejudice. The point seems obvious but I have not noticed other people making it, so thought it worth doing so.