As a father of a soon to be 12 year old girl I feel you are pushing how you think she should be living her life upon her. You are not considering what she finds interesting, only what you find interesting. My daughter earlier this year was pushing me to buy her a pink .22 rifle but I never did as I knew things would soon change and they have. She no longer mentions it. That does not mean I do not want her to learn to shoot, I do but I will wait for the day she comes to me and ask to learn.
I wanted to stick my daughter on the ice at an early age and I did. She didn't care for it and never wanted to go ice skating and I told myself that is ok. Last year she changed her mine and she is really looking forward to ice skating this season.