Is vegetarian diet healty for a 14 year old boy?

Yes and No.

It all really depends on how careful the 15 year old boy is on his vegan diet.

If he makes sure to get the right servings of fruits, carbs, veggies, and proteins, as well as vitamins he needs, he should be fine.

BUT, if said boy isn't careful about what he eats, and doesn't spend time making sure he's getting needed foods, he probably won't be healthy.

Overall, a vegan diet can be just as healthy or even MORE healthy than a regular diet.

But just like any person, vegetarian, vegan or not, everyone has to make sure they are eating enough of the foods they need, and getting all the vitamins, proteins, and carbs that EVERYONE needs to be healthy.