It seems like all the most difficult questions of faith fall along the same general line: How can a good God allow evil to exist? Why would God allow natural disasters? Why did God let so-and-so die? Underlying these questions is another one: Is God really all-powerful? Is he truly in control? If he's not, then we desperately need to rethink our conception of God. But if he is, then how can he possibly be good?
These are difficult questions. The deists thought they had found an answer when they created a God who was omnipotent but disinterested. But when God becomes disinterested and distant, everything else--Creation, sin, the Incarnation, the cross, resurrection--falls apart. You may as well be agnostic.
Part of the difficulty of these questions is the way we understand the term "allow". Or, to put it in more theological terms, what we mean when we say "God is sovereign", or "God is omnipotent". We assume that, because God is sovereign and omnipotent, then he must give his approval to everything that happens in the world. On any given day a certain number of proposals cross his desk, and he rubber stamps some APPROVED and others DENIED. Those proposals which are approved, like Hurricane Katrina or the Haitian Earthquake, actually occur, and those which are denied do not.
I hope that seems silly to you, because it is utterly ridiculous to me. God doesn't have a desk or a rubber stamp. He is not the bouncer standing at the gates of the earth. He is the King, and his kingdom is in rebellion against him. God created an ordered paradise (Eden) and gave a tremendous measure of power to human beings, who then used that power to turn on God, which resulted in the loss of order and paradise. More accurately, our sin resulted in the loss of God's direct sovereignty over Creation, because if he were to exercise his power in all its fullness, there would be no more Creation. Now, in order to spare our existence, God exercises his power in humility.
Evil, sin, natural disaster, and death are not exceptional. These are normative for a world in rebellion against its Creator. They are not punishments, they are simply the natural course of events that follow from the overthrow of God's direct sovereignty over Creation. None of these exist within paradise. But outside, east of Eden, they are inevitable.
The real "allow" question, the one that doesn't make sense, is why would God allow his son to leave the throne room of the castle and come, unarmed and vulnerable, into the rebellious kingdom. Why would God allow his son to live east of Eden, where evil, sin, disaster and death are the norm? It can only be because he loves the rebels so much that he wants to save them from the foolishness of their own rebellion.
Knowing he couldn't directly coax or command them out of it, he sent his son to be just like one of them and to die at their hands. And then the King did the most amazing thing ever--he raised his son from the dead! And by raising him from the dead, the King said to the rebels, "I forgive you for all of your rebellions and your sins. See, here is my son, whom you killed, but whom I have raised back to life! Look to him and have hope that evil, sin, disaster and death don't have the final say, but that the last word belongs to me. Behold, everything is being made new!" The one act of evil that God did allow in this world--the death of his son--is the one act by which he is remaking the world and is restoring all things to a new and glorious paradise.