Philosopher J. L. Mackie makes this case against God in his book The Miracle of Theism (Oxford, 1982). He states it this way: If a good and powerful God exists, he would not allow pointless evil, but because there is much unjustifiable, pointless evil in the world, the traditional good and powerful God could not exist. Some other god or no god may exist, but not the traditional God. Many other philosophers have identified a major flaw in this reasoning. Tucked away within the assertion that the world is filled with pointless evil is a hidden primes, namely, that if evil appears pointless to me, then it must be pointless.
This reasoning is, of cause, fallacious. Just because you can't see or imagine a good reason why God might allow something to happen doesn't mean there can't be one. Again we see lurking within supposedly hard-nosed scepticism an enormous faith in one's own cognitive faculties. If our minds can't plumb the depths of the universe for good answers to suffering, well, then, there can't be any! This is blind faith of a high order. (page 23)
I found myself twice in the last two weeks trying to paraphrase something Tim Keller said in The Reason for God about the problem of theodicy (the problem of evil). Below is the quote I was referring to.