What am I missing here - exercise increases metabolism, at least temporarily, does it not?

Kids' bodies work differently than adults'. Most of their caloric intake goes to the vastly more demanding process of growing than it does to fueling activity. It's like how a mother gains a huge appetite during pregnancy that would have made her fat otherwise.

The problem is that habits formed as kids die hard. You keep eating the same way as you did when you were 12, but have nowhere to put it all, except your belly / thighs / butt. Before you know it you're 27 and huge.