There's a concept called "conditional probability", that I think is useful here.

If all we know about a person is that they are a woman, then indeed, the probability of them getting their MBA (for example) is much lower than men.

But for a woman who has the opportunity and blessing from their family to apply to business school, THAT woman now presumably has a better probability of getting their MBA than a man in a similar situation (since, as you say, the cutoffs are easier).

Privilege is really a matter of probability. It's a measure of how likely a person is to achieve their dreams or have their desires met.

But in conversations about privilege, we often refuse to talk about the conditional probability, and only stick to huge generalizations. The probability for women on the whole to achieve all their dreams does indeed seem to be less than that of men. But the conditional probability for certain women to reach their dreams is often greater than that of certain men.