To be fair (and unfair) to the RCC, I believe there are statistics showing similar rates in other churches, it's just RCC covers it up more.
More than it being a Catholic thing I imagine it's just a position of power thing, like how celebs and rich ppl are pedos as well.

edit: I guess it's not "unfair" to point out their cover ups and stuff, but idk how else to put it.

I remember reading somewhere that some Protestants accused Catholic priests of pedophilia hundreds of years ago, and their accusations sound similar to modern accounts. I can't remember where I read that though, so take it with a huge grain of salt.

probably always, judging by the catholic church's extremely long history of doing every evil thing imaginable

it's not knowable they were covering it up

Yes. Its been a joke since the middle ages. Keep in mind most other mainline denominations have similar levels of abuse.

sex history is fun because prudes didn't exactly take down data so we can make radically different analyses that are still defensible

a couple ways of framing this:

the church for a long time wasn't very concerned with their clergy fucking people; see all the damn cardinals, bishops, popes with crops of children. you could connect that with the 'priests don't have sex' causality

change over time of the 'acceptability' of pedophilia: you don't need to go very far back at all for casual child marriage; stands to reason pedophilia could've been known and accepted in many times & places

When the Catholic Church was founded, pedophilia was an accepted and expected thing. Remember, this is the Roman Empire in the first to fourth centuries AD - the earliest Christians had to worship underground, but when the church was legitimized under Constantine it was deliberately set up in such a way that it mirrored existing Roman institutions in order to give it legitimacy. This also made sure that the families running the church were the same families running the Empire (until the split at least), and to be frank everyone was either being abused or abusing someone in the upper levels of Roman society.

So times changed and people eventually realized that fucking kids is bad, but more conservative areas held on to their old traditions the longest, including this one. Advancing in the church hierarchy involves being sexually abused, and doing sexual abuse, and it goes on for hundreds of years with most of the rest of society not really caring about it. Pedophilia is less common in the medieval world than in the classical one, but it doesn't become instantly morally disqualifying the way it is today until much later.

So the modern era comes, and pedophilia is now widely considered to be a horrible crime like no other. Individual priests are now more likely to fall in line with the societal view on pedophilia, but everyone in leadership positions knows that it's widespread because they've all either done it, had it done to them, or seen it. The Church tries to cover it all up and deal with it silently, but as noted by other commenters the Church also attracts a steady stream of abusers who are interested in having unquestioned power over kids.

So the problem doesn't go away, the Church's attempts to keep everything under wraps only increases the damage done to abused kids, and I suspect it will never go away until the church's power as an institution is completely eroded and being a priest can no longer get you a presumption of moral conduct in the eyes of the average person.

I think that ties into the problem of hierarchical institutions where the people in power only answers to those above them would inevitably becomes a hotbed for all sort of abuse.

Child abuse is most common because children have always been the most powerless group out there.