Now it is not your parents job to force food in you, it is yours. Learning to try new things without writing them off is definitely a must. I was a very picky child, I still have food issues and have not eaten red meat for many years. Look at this food pyramid to help you, lots of handy hints in there. My other advice that I give to my kids when they shop is to only buy foods that look like food. Avoid prepackaged and cook. Buy a good vegetarian cook book and start experimenting.
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Also learn to snack smart, fresh veggies, nuts, cheese. Simple foods, nothing weird at all. Nothing wrong with a peanut butter sandwich at all, but buy good peanut butter that has nothing but peanuts in it, most commercial brands are full of added sugars. Use a wholegrain bread for the sandwich, avoid white breads that add no nutrition. Waffles can be great, make them with wholewheat flour instead of white.
Oatmeal is an awesome way to start the day, maybe eat a banana and a handful of nuts at the same meal.
Iron is a huge challenge for many teen vegetarians. For that you really need to look at iron rich foods and decide which ones you can stand to eat.
Vegetarianism is only as healthy as the foods you eat.