I don't think my parents like the idea of me being a vegetarian?

Well, I'm eleven and I hate the idea of killing animals for food. It's cruel! So I decided to be a vegetarian! Now, I'm not a Vegan, I'm a Lacto-ovo vegetarian. I don't think my parents like it. Whenever I say something like "Oh, that has meat in it, I can't eat that" or say something about wanting to try vege burgers, they roll their eyes. They're meat lovers sooo. I was just wondering how I can tell them that I really want to stick to this and I want their support. Anyway, thanks for your time, :)