“An all-good, all-powerful God would not tolerate evil; thus, God either is not all-good or not all-powerful.”
This presupposes that God cannot have good reasons to tolerate evil, but he does. One is that he values free will.
The abuse of free will is the definition of moral evil. Nobody sins except by misusing his free will. Sin, in turn, can produce suffer- ing, as when one person unjustly harms another. Moral evil thus can cause physical evil, and free will can produce both. This is important because we have a good idea why God allows free will: to allow love.
The two greatest commandments are to love God and to love your neighbor (Matt. 22:36–40). Love is the fundamental thing God wants from us.
But if we had no free will, we would not be capable of freely choosing love. We might be able to simulate love, but it would be the programmed “love” of a robot, not the real thing.
It would be like Ira Levin’s book The Stepford Wives, in which a group of husbands replace their wives with robots programmed to be the perfect homemakers. The robots are always attractive, always submissive, always ready to do whatever their husbands want. But there is no love in the town of Stepford. The husbands do not love their “wives”; they treat them merely as instruments for their own pleasure. And the “wives” don’t love their husbands; they are robots with no free will.
For love to be real, it must be freely chosen, and so God has given us free will, knowing that—precisely because it is free—we may choose not to love. We may choose to act unlovingly, to sin against him and our neighbors.
God thus allows moral evil in the world to make it possible for us to choose love. By creating room for free will, he must also create room for its misuse and the consequences that follow from that. When we act unlovingly, we harm others, and this causes some of the suffering in the world.
This answer explains part of the mystery of evil, but not all of it. It doesn’t, for example, deal with evils that are part of the natural order and that aren’t caused by free will (see Days 7 and 38).