You got some good advice thus far If you have tried to reason with them and they are not listening to you then you should wear your hair however you prefer, you are old enough to make those types of choices for yourself.

parents are not always right even though some pretend they are. Your parents are sending you a very poor message about accepting yourself just the way you are by not accepting your hair the way it is and they should be proud of you! After all they are the ones that you inherited your natural curls from in the first place!
It is great that you understand your father isn't right to ask you this. Even if he doesn't know any better it is very impressive that you do.