Parents don't know that kids are trashing each other over the internet because they hardly know what social media is! If some parents were more on board with social media they would understand cyber bullying even more. Some parents don't understand that kids can cyber bully in so many ways.
Hundreds of kids commit suicide due to being bullied online, kids are not emotionally ready to become independent. My old elementary school friend Rebecca killed herself about a little over a year ago due to her parents ignorance of what was going on online. Bulling, sex, and drugs do happen to underage teens and parents need to have the right to know about ANY possible dangers that could harm their child.
I think that the parent should raise the child knowing that they will someday get on Facebook or Twitter, and teach them how to use online media appropriately. If the child feels uncomfortable due to cyber bullying or alike they can bring it up with their parent and the two of them can work something out.