I don't know if you're still around, FarFrom, but I'd like to give a different perspective on 'people hurt because they are hurt'.
People hurt because they choose to hurt. People who have been hurt know better than anyone what it's like, and can chose not to inflict it on others.
Take the example of sexual abuse of children: the majority of victims are girls; if hurt people hurt, you would expect the majority of perpetrators of sexual abuse to be women, whereas in fact only a tiny percentage of abusers are women. Women survivors of CSA are, in my experience, more likely to be campaigners against abuse of children than perpetrators of it.
I have evidence of this in my own life: my father was badly abused during a difficult and traumatic childhood. He was badly hurt, but he chose not to pass on his hurt. He chose to give his children the best life he could. There was no 'cycle of abuse' because he knew hurt, he knew pain, and chose not to inflict that on anyone, let alone his own or anyone else's children.
My father wasn't Superman, he was just an ordinary bloke from a very difficult background, so if he could chose not to pass on the hurt, so could any man.
I was also a victim of CSA - someone outside the family, no relation. So I am a hurt person, but I would rather die than inflict the hurt that I experienced on another child.