Why won't my parents let me make my own mistakes?

Okay, I'm starting to act more like a teen and my parents won't let me do what I want I understand some things they won't let me do (Like get my nose pierced although i am getting my eyebrow pierced soon) but when my mom says "Pick out a hairstyle you want" (and I was and still am into old music like Cher, Greatfull Dead(which both my parents liked when they where my age), And alot more so I told her I wanted a Style from like the 80's and her my grandmother and aunt all didn't like it so my mom wouldn't let me get it ( I understand that my mother just didn't want me to be made fun of) so I got my hair cut a different way, then she wouldn't let me get it cut the way I wanted to again so I've been letting my hair grow out and me and her are getting it cut for my birthday she tells me the same thing and I told her I want a faux mohawk which my mother and father said no too because my father well he just won't let me do anything I want to untill my mother ask why then he says he doesn't care I think he just says what he thinks my mom is going to say and my mom won't let me get it because " I got my hair cut short like that and regretted it" my Great grandmother who won't let me out of her sight when we go to town said "she (my mom) did what ever she wanted to when she was your age" she also says she just learned to let kids do what they want to or they will do it behind your back, and she is right most kids that I know would but I don't because I want them to trust me and I just don't know how to convince them to let ME make MY own mistakes they always say they did it and regretted it so I can't do it. I have told them I'm never going to drink alcohol, smoke, or get a tattoo (maybe a few piercings) but I said I'm going to collage even though I want to be a actress/director I'm going for my fall back job but that will come up in another question. My question it pretty much how to convince my parents to let me make my own mistakes and why they won't let me.