It used to be that a man went into the priesthood when he felt a 'calling'. I'm sure for some it was a desire to serve the Lord with lifelong devotion, but I think for others the calling manifested itself as an aversion to marriage, manual labor, or military, which were the only options for men for a long time. But then came more options, like office work and other not-so-manual types of labor, and the priesthood lost it's lazier population. And then about 30 or so years ago, it became okay, in certain areas of the world, to stay unmarried. No, I'm not saying that all priests were gay, only that a job requiring one to never have any romantic or physical contact with woman might attract some self-loathing gays. Especially if one's confessor framed such circumstances not as an attraction to men but rather as a distinct lack of attraction to women, and then declared the lack of attraction to women to be "the calling". But once it became okay to be gay (as is increasingly the case every day), gay men no longer needed so desperately to defend and explain their lack of attraction to women. But there are other let's call them preferences, that do need to be explained away. And to those men who also feel no attraction for adult women, come the desperate need to hear "the calling".
I am making no direct correlation between pedophilia and the Catholic Church. I do not think the Church condones pedophilia. But I do think that simply praying and denying can only work for so long. And even if it works for 40 years, you still have some pedophile molesting a kid every 40 years. And I think that when you have a career path that combines an absolute ban on adult romantic interactions, you are going to attract applicants who feel no need to engage in adult romantic interactions. In a perfect world, this would mean only devout asexual men would ever join the priesthood. But this is not a perfect world. And when you add to that job requirement the fringe benefit that no matter what you ever do to anybody anywhere ever, you can be forgiven entirely, you attract a bad sort.
Two main facets of the priesthood are that 1) you cannot have 'normal' adult reproductive urges*, at least not with normal strength, and 2) you have an unlimited number of get out of hell free cards. That's a bad combination no matter how you spell it.
*I don't consider gay urges or homosexuality to be abnormal, so don't think that's what I meant when I said "normal" reproductive urges. I do, however, like to think that gay Catholics have options other than the priesthood these days. I want to believe that rather than going out to be a priest, they could just go out to be gay. Pedophiles don't have that option, and there is really nowhere to go if you're a pedophile who wants to be good. I mean, what would happen if you just came out and told someone "Hey, I dream about diddling kids and it totally gets me hot, but I'll never do it because I know it's wrong"? How long until you've got a squad car outside your house and a neighborhood mob of pitchfork wielding parents hounding you out of town? If you like kids and you don't want to, and you're a Catholic, I suppose you'd pray a lot, confess your impure thoughts, and jump at the opportunity to believe that it's not a sick perversion but rather a misinterpreted 'calling".