How to convince your parents to let you become a vegetarian?

I talked to them about 2 years ago about me wanting to become vegetarian, and they gave me permission and even bought me soy milk and tofu. The first week was fine and I felt good about myself but the second week I got sick and they sent me home from school. I know it wasn't the tofu or the soy, it was that I had bulimia (laxatives got me sick quite often) but my parents thought it was the vegetarian diet I had had for that week.

So they forbid me to become a vegetarian and I tried to explain to them that it wasn't because of the diet but because of my loss weight diet. Anyways they told me I could only become a vegetarian when I turned 18 and by that time I was 13, now I'm 15 but I don't want to eat nay more meat, but every time I bring the subject my parents won't listen.

Any advice?