Greer also uncovers an aspect of the transgendered phenomenon that feminists really ought to find disconcerting. It’s more than just a rival victim group, but one that threatens to expose feminists’ contradictions when it comes to sex differences.

Feminists typically deny that meaningful gender differences exist between men and women, while allowing that there are some areas in which women are superior to men. Women are better at consensus building, listening, languages . . . but don’t anyone dare imply that men may have an innate edge in any hard science. Ask former Harvard University President Larry Summers how that one turns out.

Surely Greer doesn’t actually care whom Glamour magazine honors as woman of the year. (Aren’t old-school feminists supposed to object to such beauty-obsessed rags anyway?)

Yet what happens when transgender women start competing against plain old women in other areas of life? Say, in tennis matches and swim meets?