Interesting point. When I was a Bishop in the LDS church, I had a few cases of pedophelia from the last people I would have suspected — people who teach children, serve in Scouts, are sports coaches, etc. Without ever really thinking about it, I always assumed those occupations were filled with angels.
The General Authorities were casually blunt about it: pedophelia cannot be cured. What? These were men who thought gay men and women could change their sexual orientation.
So I checked with psychiatrists. They said emphatically, you cannot change a pedophile; you can only protect children.