They are protecting their little girl from the Big Bad World. As a parent of a daughter myself, I can tell you that they have good intentions.
The best way to get your parents to allow you more freedom is to do more responsible things and to display it to them.
You can do one of two things or even do both:
Start them off easy.
If they don’t want you to go out and especially if you have never been out without your parents, talk to them and say you are going to meet some friends at a restaurant. Then ask your dad if he can drop you there and pick you up after. They will most likely feel more relaxed if they are allowed to be involved in your first outing and that they know what time you will be home.
After a few weeks of this, you can tell them your friends are picking you up at home and that you will be home at a later time than usual. That you don’t want to inconvenience your parents and that you promise to be home on time. Make sure you stick to your promised curfew and if you can’t then make sure you keep them informed on why you will be late.
Once they are more comfortable that you can handle being out in the big scary world they will eventually loosen their grip.
Go in for the kill
Ask your parents for funding to start your own law firm or business. Work on your business day and night. When you want to go out you justify it by saying that its for business meetings and networking. They will want you to make a success of yourself. You will have meta-morphed from their little girl into a responsible woman with a vision, and who can look after herself and after her business. Your parents will be so proud.
Two birds with one stone.