3 Reasons for:
When you get the balance right, it's a very healthy diet indeed. Far healthier in comparison to a meat intensive diet.
There are so many possible ways of cooking and preparing vegetarian meals you can have a lot of fun tweaking recipes to find out what you like.
It's far cheaper than eating meat.
3 Reasons against:
Your farts will smell really bad.
There's no real substitute for meat. You'll meet so many vegetarians claiming that quorn/meat free products are just as good as meat, but they're just being ignorant and only deluding themselves. If you find you're eating 'quorn bacon' or anything labelled as imitation meat then you're a plastic vegetarian who may as well just eat the real thing rather than processed fungus which is about as healthy as eating at Burger King.
If you don't properly plan your meals, you'll wind up being undernourished and ultimately unhealthy.