It sounds contradictory: Young people, we’re told, are having less sex than older generations did at the same age. But they’re also contracting more sexually transmitted diseases than any other group, and the rates of infection are accelerating at an alarming pace.

Last year, combined cases of syphilis, gonorrhea and chlamydia reached an all-time high with half the reported infections occurring in adolescents and young adults ages 15 to 24.

The...