When my cousin Juliet and one of her friends, both eighth-graders, joined the women’s weightlifting team at their school, I was astonished. When else in history could such a thing have been possible? The girls had done it, Juliet explained, “because we wanted to start a new sport that would make us stronger.” It is a simple goal, but it says a lot about our remarkable moment in the history of fitness.

When I was her age (I’m now 47), a girl wanting to get stronger might have provoked snorts of disapproval and mockery, even...