How to let my parents know that I wanna make my own choice?

Okay so I am homeschooled, 16 years old and I hate it. But theres nothing I can do about it. And e ways, im starting college soon and because im still under 18 im still at home. I was planning on leaving at 18 because me and my bestfriend were ganna room at ut @ austin. (I went to public school until the 8th grade) and e ways, my parents told me they dont want me going to austin because it’s like a party town or something. I wanted to be a vet, but im not to good at mathematics, but im workin on it. My mother told me that me going into vet school seems very unlikely and that I should stay here in this sh*tty town (she didnt curse lol) and just go into a nursing program like my older sister did. The thing is I dont wanna be a nurse and since im the baby out of my family (3 older sisters) my mom wants me to stay near home. I’ve tried explaining this to them and they refuse to listen. My parents told us all that after we graduate we stay 2 or 3 years at home and then we’re allowed to leave. At 21!!! My oldest sister did that and she has a very good job as a nurse now and is making a very good amount of money, however I dont have the patience to stay here until im 21. I’ve been dying to leave since I was 14. Help?