Shortly after arriving at the University of Virginia, in the fall of 2013, Taylor Gestwick made an appointment at the counseling center. He had suffered from depression since ninth grade and had never previously sought help. He didn’t tell his parents about his therapy sessions, partly because he didn’t want them to view him differently. "My one condition for being there was my parents’ not being involved," said Mr. Gestwick, now a sophomore. "I know that if I would have known my parents would have been told regardless of my opinion on the matter, I wouldn’t have gone to seek help."