It could be some manner of centralized belief or ordering… But I somewhat doubt it is that widespread. IE - not all pedophile priests are satanic cabal.
First is the issue of pedophilia. We often refer to it as attraction to someone who is underage - which is often the legal age of 18. This is the age of consent in many states and nations - and thus statutory rape occurs when sex with minors occur. However, girls begin to hit puberty between the ages of 12 and 15 - developing physical characteristics of adult women. The age of consent exists because we believe it to be improper to engage in sex at that young of an age, as people of that age are not properly prepared to make such decisions. Attraction to girls who are in or past puberty, regardless of their chronological age, is not technically pedophilia - which is attraction to individuals who have not yet entered puberty.
This conflates the issue of sexual misconduct and statutory rape among teachers, clergy, etc with the issue of pedophilia among those same groups.
Teachers and clergy carry power/authority within the minds of the young and impressionable. It is not surprising that there would be plenty of instances where an adult surrounded by younger people, entering their days of sexual awareness, would find both desire and opportunity to fulfil the proverbial lusting loins. It's also not surprising that exists within a gray area of consent and confusion - some of which is actually preyed upon.
What is unusual is when those prior to puberty are placed into sexual scenarios. That, I would argue, is the real metric to isolate from the reports and track down.