A common attack from everybody angered by this outside the church (and by quite a few decent Catholics inside, obviously) is to ask: why not open the files to the police, at the very least where they have asked for them? So that the criminals can be subject to the usual course of justice? Fair point.
The purpose of my post here is to argue that the problem for the Pope is that this would undermine Catholic doctrine. Hear me out.
Fundamental to Christian doctrine of all flavours is the idea that no matter how terrible a sinner you are, your heinous actions have already been paid for by God's giving of his only son Jesus to pay for the sins of mankind. Of course, doctrine varies from denomination to denomination, but the philosophy of forgiveness is universal in the Christian religion, and in many ways it's quite a nice, cuddly thing, because it means that everyone can have hope, no matter how terrible the things they have done are. But it has always struck me as very much a double-edged sword (including when I was a very ardent, if rather strange, mixture of evangelical/Presbyterian Christian during my teenage years), for precisely the same reason. It means that intellectually, there is no sin you can commit that God will not forgive if you are repentant. And, at base, that's all it takes: feeling a bit bad about it and asking God for forgiveness. Even if you've committed those sins that the 'non-Christian world' (if you'll allow me to put it like that) would perceive as unforgivable, such as raping small children. There is more rejoicing in heaven over the one sinner who repents than the 99 people who've been lovely to everyone all the time (I paraphrase). I've always thought that was a bit of a flaw with Christianity.
Now, many denominations of Christianity take a more worldly, realistic line on this aspect of the basic Christian philosophy, and I don't imagine many of the clergy of the Church of England, for example, would feel uncomfortable about reporting a fellow vicar for such a crime - but the Catholic church institutionalises the doctrine of forgiveness in an unusually strident form via customs such as confession, for example. It's even a bit of a trope of many books and films that the seal of the confessional is so sacrosanct that if a Catholic priest takes confession from someone who has killed, for example, he is supposed to give absolution - perhaps encouraging the killer to report themselves - but then ultimately, to carry the knowledge of it without spilling the beans. However that plays out in real life, it is technically true. And I suspect it has happened.
And into this comes, inexorably, the doctrine of priestly celibacy.
Now, decent Anglican men and women (for example) are evidently not put off following their vocation to become a vicar by the knowledge that they will be required to sacrifice Earthly love, sexual intimacy, or the joy of having children - but obviously many decent Catholic men will be (and women don't even get to ponder the issue, of course). I'm sure that the majority of men inspired to take up their vocation to become priests are decent human beings, but quite obviously, many indecent Catholic men have also spotted an opportunity to take advantage of the traditional deference to the priest to abuse children. But because in terms of strict Catholic doctrine, nothing is technically unforgivable, they know they'll have both an opportunity and an out. And because of the doctrine of forgiveness as well as the political realities of the modern Catholic church, they know they will be protected.
The Pope has thus found himself in an impossible position: 'betray' his fellow clergy to the police, thus weakening the church via both public scandal and the surrender of his Godly authority to an unthinking secular institution that does not share God's values of forgiveness - or else try to keep it secret so no-one worries about it, and sort out the problem in-house.
Frankly, I wouldn't like to be in his shoes.
But then again, I'm one of those dangerous aggressive atheists.