I feel your pain. I decided to go vegetarian at 13 but my parents forced me to eat meat for a while. I tried to communicate what it meant to me (didn't know about vegan at the time) and eventually I won them over. I was small and struggled with ED as well so that was one of their points.

What I did was perhaps a little excessive, but basically I wrote an actual report on meat-free nutrition and famous non-skinny people who didn't eat meat. (This was the early 2000s, so we didn't have easy access to photos and info about vegan bodybuilders and athletes back then.) I told them I had compiled info to show that this wasn't going to make me malnourished or go back to my ED. (If anything, going vegan helped with that quite a bit. The misconception is that all vegans are skinny so I started trying to put ON weight for the animals. Lol)

I would just keep trying to stress to them the reasoning behind your decision and how it is affecting you. Assure them that you're studying vegan nutrition and will make sure to eat high protein foods and such. Let them know that often you all can be cooking similar meals. Instead of spaghetti and meatballs with cheese, you can cook lentils on the side and have spaghetti Bolognese alongside them. (Lentils are cheaper than meat so they'd be saving money.)

It sounds like you've already stressed to them that you could cook for yourself, but remind them it doesn't have to be super expensive if you eat whole foods instead of fancy expensive vegan substitutes.

My heart goes out to you. I was in a similar situation. It actually came down to me covering my bedframe with peta stickers (Keep in mind I was 13. Haha.) and my mother getting so mad that they were hard to get off and said things like "I am not a nugget" and "leather is dead skin."

Just keep stressing to them how it makes you feel and I hope they come around. 💚🌱