If they the majority cannot convince you not to be a vegetarian, then what make you think they should accept you for being one? Would the situation be any different if you want to eat meat and they are vegetarians and say no? It's all the same.
You can talk to them, show them facts and figures etc all you want but if they don't want to accept it, they won't. And should not be made to.
If you are a minor living at home, you can ask your parents, If they say no, then it's a no. If they yes but with a set conditions then follow those conditions. And make sure you keep your end of the bargain.
Besides, they may know something about you that you are not saying here. It will really boil down to your intra family relationsahip and how things are done in your house.
PS If you are under parental care and responsibility and you refuse to eatassome suggest, they can have you confined and force fed if it becomes a medical issue.