Isn't it obvious?
#1. Most kids won't talk to their parents about sex. Are you fucking kidding me? So asking for birth control is not going to happen.
#2. Kids are going to fuck. There is nothing you can do, short of castration, to stop them.
#3. Given that 1 and 2 are facts, kids are going to get pregnant and for holy fuck's sake, we don't need anymore teenage parents!
To sum up: requiring parental consent for birth control = unwanted babies.