My mom was always pretty happy to hear I was too busy to make many jumps ("you haven't been skydiving, have you?"), BUT whenever she introduced me to someone, that person would say, "oh, this is the skydiver!" Parents want their to be safe and live forever, but they also love to brag about the cool things their kids do, and how their kids are more adventurous (or whatever) than all the other kids. And they want their kids to feel joy and passion.
You might talk to your mom about how skydiving will set you apart from the other applicants for college and grad school (it really will, especially if you learn to talk about how what you learn about yourself and human nature in the air, applies in daily life and in school), and that it will HELP you achieve the goals you have that she supports. Then follow through on that.
If your plan is to become a DZ bum once you finish high school, that's going to be a tough one to sell, lol