Personally I don't think anyone younger than 21 should partake in an extreme diet at all. Let the body finish growing and maturing before messing around with it.
There's something I've always been a bit confused about on this topic. Human beings developed/evolved into being omnivores. Our bodies need everything, including meat, in order to be healthy. The best thing anyone can do is to keep a good balance of every food group in their diet. Any extreme shift one way or the other will only end up damaging to ones health.
Vegetarianism isn't as extreme as, say, being a Vegan so it's not as dangerous. All you'd need is a few vitamins and supplements to make up for what's missing and you should be ok. Being a Vegan (or a pure Carnivore, for that matter) puts you at serious risk because you have to maintain a very complex regimen of supplements, vitamins, and often medication, to keep from ending up in the hospital. Or worse.
Anyone contemplating an extreme diet should first check with a doctor and a nutritionist so they will know what needs to be done and what risks are involved.