How to convince my parents to let me do gymnastics?

For a really long time now, I have wanted to do gymnastics. I am constantly in awe of all of the gymnasts I see on TV. The problem is my parents won't let me take classes. They've told me its because the coaches will tell me I need to be skinnier and they don't ask the exposed to that. I totally get that but on the other hand that stuff doesn't really bother me. I just want to do gymnastics because I feel I would genuinely enjoy it. how do I convince my parents that that stuff won't bother me?