From a philosophical perspective there are two "arguments from the problem of evil."
The first is the "logical problem of evil."
It can be expressed in the form, "if there is an all powerful good being who hates evil, then evil should not exist." Since it is obvious that evil does exist, the arguer concludes that an all powerful, good being does not.
Philosopher Alvin Plantinga has pointed out that the propositions are too absolute. A more nuanced argument would say that, "if there is an all powerful good being who hates evil, then lacking good reason, evil should not exist." The conclusion then may be stated, either there is no all powerful good being, or that such a being has reason to allow evil to exist.
Do we know why evil is allowed to exist? Some people have theorised and hypothesised. They may be correct or not. Is it possible that an all knowing being would have reasons that we wouldn't know? I'd say that was highly likely.
Although this seems like a simple argument, in philosophical circles it was considered dynamite. Even atheist philosophers have conceded that Plantinga robbed the logical problem of evil of any force.
The second is the "emotional problem of evil."
This is our gut reaction to events like the Japanese tsunami. "Why God, why?" It has force because we are human beings and we empathise with other human beings, however it has a flaw that destroys it as an argument.
The atheistic world is one of brute facts. We are not headed for a destination. There is no "ought" to the world, no way that it should be. There just is. It is what it is, to borrow a phrase.
When we describe something as evil we are making a value judgement. We are saying that there is a gap between what is, and what ought to be. The Christian can say, "yes, there is something wrong with the world. Things are not as they should be." What can the atheist say? Remember, there is no "ought" in atheism. "I don't like tsunamis?" I don't like mashed potato. Preferences only describe our reaction to something, they say nothing about whether it is right or wrong.
The atheist is hoisted on his own petard. The very fact of saying that "things ought not to be this way" is an argument against his atheism. What is supposed to be a problem for the theist is turned into a problem for the atheist. It also demonstrates how incoherent atheism is when measured against actual human experience.
Fortunately for atheism rationality isn't a prerequisite.