Consider the enormous advantages that say, President Obama's daughters have over say, an Asian girl from a economically disadvantaged family. Yet the check marks that each would mark on a college application would result in the President's daughters getting racial preference.
Or consider two students from the same socioeconomic background (perhaps even attending the same high school), but one is white and one is black. Under affirmative action, the white student would have to perform at an exponentially higher level to receive the same consideration. As long as race is a consideration AT ALL, then the playing field isn't level.