Mine said no as well, but I didn’t care it was my choice. After all it is my body I should have a say so as to what goes in it. I just stopped eating it, my mom would put it on my plate, and I would leave it there. She eventually got the hint.
If you want to be a vegetarian you can do it! When I told my parents they got really mad at me and said I was being stupid. But when I stopped eating meats, they got used to it. I also showed them “Meet Your Meat” and they understood (at least somewhat) why I wished to be a vegetarian.
Just show them that vegetarian meals are healthy and you do get the essentials without eating meat. I’m sure they’ll understand and good luck!