I think the best thing a teen can do is to find lots of information for their parents about vegetarianism and especially it's health benefits (eating lots of vegetables and less meat can lower your cholesterol and help prevent heart disease and cancer, for example.) Look for reputable studies that show documented evidence.
I wanted to become a vegetarian at age 12 but was forced to eat meat because of family pressure. At age 18 I finally became a vegetarian and even then faced lots of family
resistance. My mom continued to try to feed me meat. For my 19th birthday, she cooked a meat lasagna! I'm now almost 30 and still vegetarian, and although the family resistance continues, it has lessened a lot. Since my grandfather had several heart attacks my grandmother even subscribed to Vegetarian Times to get some ideas about how to cook different vegetables.
One thing you should be careful to watch is that you eat a variety of healthy foods. If you just eliminate meat from a traditional "meat and potatoes" diet...all you're left with is potatoes and nutrient poor foods like iceburg lettuce. I became anemic at first because I didn't start eating foods like lentils, dark green leafy vegetables, beans, tofu, and dried fruits. (All these foods are rich in iron, which is really important for a growing body.) This can be even harder if you're not involved in the cooking of the family meals.
So, good luck. Do lots of research and maybe you can even help your whole family to improve their diet in the process!
