The Problem of Evil ... and Good

If it weren't for logic, atheism would make a viable worldview.

Quick example: Christopher Hitchens in his book, 'God is not Great' summarizes a classic argument against God's existence known as 'the problem of evil' on pg 268:

"Is he [God] willing to prevent evil but not able? Then he is impotent. Is he able but not willing? Then he is malevolent. Is he both able and willing? Whence then is evil?"

Then, 30 pages later, when discussing moral relitivism, Hitchens makes this statement:

"There is no such thing as evil, and those who argue with me on this point are wicked, stupid, or both."

Now, I'm no rocket surgeon, but if there is no such thing as evil ... how can you use the 'problem of evil' to argue against theism? Moreover ... with no evil, there's no such thing as good; with no good, there's no such thing as great; with no great, how am I even supposed to understand the title of his book?