I think it's absolutely fine to not want children - and to stay 'child free by choice.' But to try and get yourself sterilised at like, 19, 20, 21 (like a few posters have suggested,) is absolutely ludicrous. No wonder it's not allowed. Whilst I'm on the OP's side, and think her partner is actually practically bullying her, I'm really against anybody having sterilisation under the age of 30, to be honest with you.
Many women I know, including myself, were adamant that we never wanted children. Even when I married my husband in my mid 20s, I was still never wanting children. He didn't want them either. Then he started to get a little bit maternal and around 27 to 28 years old (we are the same age.) I still didn't want them.
Then suddenly for some reason I hit 29 and then bang, I suddenly started to look fondly at the children of my friends, and family members, and work colleagues, and started to get this massive, massive surge..... of maternal feelings. I started to develop feelings and emotions that I never knew existed.
I'm not saying everyone is going to have that, and it's fine NOT to. But you MIGHT do. And I think it's absolutely ridiculous to be sterilised at 19 to be honest. Because as I say - myself, and dozens of women I know (who didn't want children,) got to between 27 and 32 years old and suddenly had a massive maternal urge.
I don't think sterilisation should be allowed until 35, to be quite honest with you. If you're not wanting them by 35, there's very little chance you will change your mind and want them. If you're not wanting them at 25, (or under,) there's a good chance you WILL change your mind by 30-ish...
Same goes for men. Having a vasectomy at 20 or something is stupid. As I said, my DH never wanted them, and then got to 28 and BAM, he had a desperate desire to be a dad.
And don't even think about mentioning 'a sterilisation reversal...' because in many cases they don't work!