Another reason people like to cite in opposition to pedophilia, is that because children do not have the mental capacity to consent to sex, the whole thing is suddenly foul.
Children don't have the mental capacity to consent to any number of the things we inflict on them, and certainly don't have any sense on the discipline available in their homes, what they can or cannot eat for supper, if they're allowed to go to school or what they're allowed when they get there, what they should do in their spare time, what entertainment they're allowed, et cetera. Since they already unable to appreciate the reasons for these things and make informed decisions, and parents/the state are allowed to decide, on their behalf, what's good for them, it makes no sense to deny a state or the parents the right to decide whether or not a good molesting would do well by their child.
I mean, Hell, you couldn't legally just shove a stranger in a corner and hold him there against his will. And yet you can give your kid a time out, if you want, and I think if we're going to have a double standard about being able to force people a certain age to do or not to do things, we should at least make that a consistent standard. Really, make exceptions for all or exceptions for none.
Pedophilia should be treated, generally, in the same fashion one ought to treat a knife. A knife is, in and of itself, a tool that can be put to certain ends, and while the tool itself is not moral or immoral, the end certainly can be. The same applies to pedophilia.
For instance, you can use a knife to cut your steak with or to hold up a bank - the former being a good end, the latter being a terrible one. The rape of children ought to be thought in the same way. So, for instance, you could use pedophilia as an affordable form of discipline or punishment, or could just use it to deliberately inflict harm on a child.