The question is whether the terrible suffering in the world – and the amount of suffering in the world is terrible – is incompatible with the existence of God. I think the answer of whether it is incompatible is clearly no.
In the 1970’s, I wrote a book called ‘God, Freedom, and Evil’ in which I talked about the free-will defense. By use of the free-will defense, you can show formally that there is no contradiction between the proposition that there is such person as God who is omnipotent, omniscient, and holy-good on the one hand; and the existence of suffering, death, evil and the like on the other. But that is not the whole of the question.
Philosophers who wanted to say there was a real problem for believers in God then turned away from the claim that there was a contradiction, instead to the claim that the existence of God, as an all-good God and so on, is unlikely or improbable given all the evil that there is in the world. The suggestion goes, “well maybe there is no contradiction, but if you see how much evil there is, you can’t sensibly also believe in God.” That claim too is very hard to make out. Philosophers have been trying ever since the 70’s to state this probabilistic version of the problem of evil in a way that really works. My inclination is to say that nobody has succeeded at all. It is very difficult. It gets much messier than the original straight claim of a nice clean contradiction. So I do not think the probabilistic suggestion works either.
Of course, Christians and other believers in God do have something of a problem with the existence of evil. Even if there is no contradiction and even if the probabilistic argument does not work, why does God do that? God is holy-good, but we see the terrible things that happen in our world. I think the answer has to be, in the long run, that we do not really know. We do not know why – at least in any detail – God permits the evil that he does.