You see them at night in big cities: men dressed up as women, complete with makeup, jewelry, and high heels. Despite their best efforts, it’s not a pretty sight. Nor is the sight of men who take a more drastic step: undergoing so-called sex-reassignment surgery. When these surgeries were first performed at Johns Hopkins University in the early seventies, one psychiatrist—Paul McHugh—started asking questions about the wisdom of this. After all, the outcomes were not women, but grotesque caricatures of them. When McHugh became psychiatrist-in-chief in 1975, he decided to test the claim that men who underwent sex-change surgery were...