Way too simplistic. There are a thousand reasons for parents to hate pedophiles, of which the need to control children is only one, and usually not a conscious one. I think most of it can be chalked up to the moral panic itself, though. But there's also the fact that parents have an interest in safeguarding their genetic legacy, and sexual abuse threatens that because sex with children--especially girls--can damage their insides. With boys it's probably more a fear of screwing them up sexually so that they are less likely to have children (the homosexuality as infection theory)--I'm not saying it's right, just that it exists.

There is also the fact that parents fear their own potential to harm kids sexually, so they compensate by projecting their fear and self-doubt onto anyone who makes them think about kids in a sexual light (as pedophilia forces them to do). It threatens the family dynamic. I could list dozens more off the top of my head, but a) they would likely be minor, and b) they are more about the science of genetics and things like that and are more complex than I really want to get into here.

And the 'they want to control their kids' lives' line is really the mantra of the pro-contacters because it allows them to think of parents as the enemy, but it is simply a minor consideration. Most parents don't want to control their kids for its own sake; they just want a) their family to run smoothly and b) their kids to be safe and secure, and they generally allow kids freedom to the extent that that's possible.