I was brought on a trip as a teenager in Boy Scouts. I'm so thankful I went. I learned a lot on that trip both about me and the outdoors. It also hooked me and I've been going almost annually ever since.
Now a days I'd bring a teenager to show them what the wildnerness is and what its all about. Show them why it needs to be protected. Show them the stars at night, the smell of bacon on a campfire and the sound of a loon. ALL of those things can change a person for life (usually for the better).
They usually wont realize how nice it is to get away from their computer, phone, video games etc. However they will learn that they can get by with out them and have an awesome time.

For some of them it will be their first chance to pee in the woods (exciting I know  ;D ) It is the experiences like that that can have a profound impact on them.

Make carrying gear a challenge and they will rise to the occassion.
Bring LOTS of food though :P

All of this BTW coming from someone who isn't too far past his teenage years.