Because this isn’t what is actually on the Antiracists’ mind. The call for people to soberly “acknowledge” their White Privilege as a self-standing, totemic act is based on the same justification as acknowledging one’s fundamental sinfulness is as a Christian. One is born marked by original sin; to be white is to be born with the stain of unearned privilege.
The proper response to original sin is to embrace the teachings of Jesus, although one will remain always a sinner nevertheless. The proper response to White Privilege is to embrace the teachings of—well, you can fill in the name or substitute others—with the understanding that you will always harbor the Privilege nevertheless. Note that many embrace the idea of inculcating white kids with their responsibility to acknowledge Privilege from as early an age as possible, in sessions starting as early as elementary school. This, in the Naciremian sense, is Sunday school.
Think of it. A certain class of white person, roughly those who watched 30 Rock and Mad Men, lustily pumps their fists at the writings of a Coates who says that he is surprised that white people—i.e. ones like them—are interested enough in black people and racism to even bother reading his work. Coates is telling these people that they are sinners, in a sense, and they are eagerly drinking in the charge, “revering” him for it. This, ladies and gentlemen, is worship, pure and simple.