But the issue here isn’t a coal miner v. Harvard graduate, it’s a female student at Yale v. a male student at Yale. (And BTW there ARE support group and special opportunities for first gens at Yale).
Societies aren’t defined by the existence or non existence of privilege, but by the ways those with privilege find ways to make privileges accessible to others rather than caste-based, gender-based, etc., or by the ways those with privilege find ways to keep others from approaching them.
Humorously, it’s said that the French revolution abolished privileges for a few (which were an official category of things, laws, rights, etc.) so that most could have their own special privileges. 