I don't know why we keep expecting men to get it. Seriously, it's rare for a white man in a position of power, even those who are supposedly enlightened to get their privilege. It does happen, for example, my current boss is an awesome mentor to graduate students of all genders, races, and so on, but it's rare. In some sense I don't blame them, privilege is difficult to see. As a white woman I rarely notice my white privilege, except when a person of color talks about their experiences of discrimination.
It really isn't that mysterious. Imagine older, male mentor and young, somewhat geeky, but still "nubile"(I hate that word) female grad student working long hours together in the lab or slaving over ancient tombs. If this was a movie, what happens next? William Deresiewicz knows.
If you were an older male professor faced with uncomfortably attractive young grad students, what would your reaction be? Make sure the office door stays open. Whatever you do, don't go out to drinks after work. Keep things professional. Would the same be true with your male grad students?
I know, I'm being hetero-normative, but it's not a question of actual impropriety, it's just appearances. The point is the privilege is invisible. You are a male grad student and you "hang out" with your adviser. Your adviser thinks of you as a younger version of himself, people who are different, who think differently make him uncomfortable. Most likely he doesn't realize this. He can't help his feelings, but they affect his attitude towards his students, how much time he spends with them, how enthusiastic he is.
I happens, even when there is no conscious intention to discriminate. Networking opportunities become limited. Older faculty are uncomfortable. Young men and women don't see what's going wrong.