We Never Know
No Slack
Regardless if they are born pedophiles or not, it's a paraphilia that somehow develops, and not all pedophiles act on those urges. It's like a mental illness and it should be treated like one. If you're to execute people for immoral actions, what good is that for those who have urges for immoral actions but are trying to resist it? It would make more people who have these urges afraid of getting help afraid of being demonized by society for having these urges in the first place.
I think the confusing part of it is the tendency of people to call child molesters pedos, and saying 'pedophiles should be executed' rather than 'rapists should be executed'. There is certainly a difference.
"It's like a mental illness and it should be treated like one"
If you think pedophilia(sexual feelings directed toward children) is a mental illness, are there other sexual actions that you think are caused by mental illness?