The french philosopher Pierre Bourdieu discribed multiple forms of "capital" any individual can accumulate in order to get successful:
- economic capital (actual money, houses etc)
- social capital (the contacts you have to people who can help you out)
- symbolic capital (your ability to simulate a certain socioeconomic status in a way so others belive you are also from their class of society — so the way you look, dress, speak, what music you listen to etc)
- cultural capital (the actual knowledge you accumulated by learning, reading, practise etc)
The more any individual has in each of these categories the easier success is going to be for them. Many of these categories have a huge inherited part as well. Even if your parents are poor academics for example they might teach you how to speak a certain upperclass language, have good contacts and cultural capital for example.
Black people in the US have had a (much, much) worse starting point in all of these capital forms and some of those deficits will effectively bar anybody from that socioeconomic background from studying, even if they are a very talented person.
Quotas like these are the recognition that existing cultural biases are instutionalized and you have to counterbalance them to a degree, just to make them fair.
If you ran a marathon and the guy next to you was not only held back for 30 minutes at the start, but also had to carry a bag of bricks and learn a new language while running (and none of that by his own choice), you'd hardly complain if the guy's run was judged in a different way than yours, or would you?
This is essentially what something like this boils down to. People from a poor socioeconomic background cannot lean onto their or their parents contacts (lack of social capital), they cannot lean on their or their parents money (lack of exonomical capital), they cannot lean on their sophisticated way of expression (lack of symbolic capital) — they in fact have to learn that new way of expressing themselves if they want to be taken seriously — and they cannot lean onto their cultural capital as people from rich educated families will naturally have a headstart here as well.
Societies with less steep socioeconomic divides tend to be safer, more productive and happier, so it is only rational.