The entire problem is that we categorize people into different buckets. "White", "Black", "Asian", etc. Admissions must be race blind. In general our society must be race blind. "White" people were once Polish, Italian, German, etc. Yet these identities have melted away over generations in large part because society did not and does not actively reinforce these identities. By forcing people into these buckets we rein…
So how do you make that right without continuing to use the buckets? The only way is to either completely dismantle Capitalism, and start over with it or something else again from scratch were everyone starts on even ground again, and it never mattered what bucket people were in. The simpler option is to use the buckets and say that people in the Black bucket get special benefits at the cost of people in the White bucket to right the wrong that happened, and this needs to continue until they're close to even again.
It's like if a friend steals money from you. The only way you're likely ever going to fix that friendship is if the friend at the very least gives the money back and apologizes. Pretending like it never happened isn't going to work.
An additional thing is that you still have people using the buckets for their benefit, or just because they don't know better. In order to counteract the actions of those people, and recognize who's hurt by them, you have to also use the idea of the "buckets".