Can you ask them for a trial period? Tell them that you'd like to try this for two months. Make sure they see you eat loads of vegetables and healthy foods. I cannot imagine denying my child that, even if she wanted to be a vegan. I'd at least let her try it and have sensible discussions about it. I actually became a vegetarian in high school. My mom said that if I didn't like what was for dinner, I had to fix my own food. Sadly, I was rather malnourished at the time, but I am grateful they gave me the space to be my own person. I wasn't drinking, going out with boys, or into drugs. All teens want to assert some indepdence. Better with food than drugs!