The anorexia problem is part of the obesity problem. Young girls (and increasingly, young boys) see all the pressure to be skinny and at the same time are surrounded by food designed to make them fat. They respond by swearing off food entirely. They are terrified of becoming fat, and literally see their bodies as fat even as they are about to die of starvation.

Fixing the numerous causes of obesity would definitely help. But it's not made easier by the existence of "pro-ana" social media which encourages young anorexics to reinforce each other's dangerous attitudes to food.