“I have friends with debilitating problems like cutting and OCD [obsessive compulsive disorder],” a girl named Jordan recently told us. “It’s frustrating because I can’t help them. I mean, I’m only 14 myself.”

Young Americans have become unwitting guinea pigs in today’s huge, unplanned experiment with social media, and teenage girls like Jordan are bearing much of the brunt. In conversation after conversation, adolescent girls describe themselves as particularly vulnerable to the banes of our increasingly digital culture,...