Pedophilia is one of those subjects that people dread discussing. Our ability to understand it is obstructed by our general level of disgust towards it. For this reason, I ask that you develop a curiosity and a willingness to remain completely open minded so that understanding can evolve as a result of it.
Long story short, the pedophile was hurt so badly as a child, that his or her entire child-ness and innocence had to be suppressed, denied and rejected for the sake of emotional, mental or physical survival. There is therefore an aspect of them that had to grow up way too fast and thus could not develop naturally. As a result, there is a part of themselves that they dissociated from that is frozen in a state of childhood. As a result of dissociating from their child-ness and their innocence, in order to feel whole, they must reconnect with that aspect of themselves that was lost. This is why they are attracted to children.