Don't let your parents discourage you! Maybe they are having a hard time letting you grow up and realizing they will not to able to "control" you much longer. Making and elephant out of a fly in their attempt to hold on to their "little girl".
I agree with the previous posters, stay calm and explain , if necessary over and over why you will wear your hair like you want to! Parents a can be a bit dense sometimes, I know I am
You will find plenty support on this site, I think there is a thread similar to yours in the curly teens where her dad did not want to give permission for a drivers license unless she straightened her hair for a family photo.
Stay strong, I believe you can convince your parents to let you be who you are!
2c/3a cg 01/10/13

Hair Properties: low( first 4 inches) / high porosity, medium density, fine/medium texture Climate : hot humid summer, coastal GA

Co-wash: Suave Naturals Coconut / Everlasting Sunshine, V05
Rinse out :Tresemme Naturals Nourishing Moisture, VO5 ocean refresh
Gel: La Looks sport, Volumax mega gel,Biosilk Rock Hard gel my HG

Love ACV , pedaheh's gelatin treatment
My hair hates everything Deva curl and Curl Keeper,