> This also means that on average, a man on campus is more qualified to be there than a woman on campus

This does not follow from what you wrote before. I think it would if equivalently talented men and women were equally likely to apply to Caltech. This does not seem to be the case, since as you say not as many women are applying.

I'm going to make up some numbers for an analogous problem which might make the logic more clear. Let's say the top 50% of men in a year apply to some university, while only the top 10% of women apply. Assume there is some randomness in the admissions process (because frankly there is), then a randomly sampled woman who was admitted is likely to be a stronger candidate than an average man who was admitted.