When math majors were assigned advisors at Prestigious University, Jane was the only one whose advisor wasn't a full professor. Her advisor was a postdoc, and was the only woman among the research faculty. There had never been a female tenured or tenure track professor of mathematics at Prestigious University, and Jane's advisor was the first female math postdoc.
Jane was miffed that her advisor was temporary faculty who would soon leave, while everyone else's advisors were long-time established professors who had much greater familiarity with the courses and with the culture of the department. Jane tried to convince the secretary who made the assignments to reassign her to a full professor, but the secretary thought that it would be best for a female student to have a female advisor.
Not surprisingly, the postdoc's knowledge of the department and the university weren't very deep. Neither Jane nor the postdoc found much to say to each other. And it wasn't fair to the postdoc to have to take on the extra burden of advising an undergraduate. The male postdocs didn't do that.
While I appreciate what the secretary was trying to do, I'm not a big fan of the idea that we should expect women to be better mentors for women than men would, and men to be better mentors for men than women would. At Prestigious University, it was the professors' job to advise students. If they were doing a better job advising men than advising women, then they weren't doing their job.
If a male doctor gives better medical care to male patients than to female patients because he feels empathy for people who remind him of himself, then he's not doing his job.
This story about a Harvard researcher going the extra mile for a patient because they were both women of about the same age reminds me that there's still work to be done in empathy training. We need to teach ourselves not to just mentor, hire, or promote people who remind us of ourselves, and not to give favoritism to colleagues because we share their nationality, gender, religion, race, etc. If we're going to get along with each other, and have the sort of world we'd like to live in, it's important to learn to treat everyone fairly and well.