I was rereading Christopher Hitchens' best seller God is Not Great recently and going over some of the arguments he makes. I first read his book in the summer of 2010 when I was on vacation in Asia after I graduated college, and since then I've acquired a great wealth of information learning about religion and debating with theists.
One interesting thing about Hitchens' approaching to the debate was that unlike Richard Dawkins, Hitchens was not all that concerned with disproving god. It was religious belief, and its ill effects that Hitchens was primarily after, not so much the ontology of god. That's why when he debated religious opponents, he did a much better job when the debate was centered around the social effects of religion such as, "Is Christianity Good for the World?" or "Is the Catholic Church A Force for Good?" or "Is Islam A Religion on Peace?" However, since Hitchens wasn't a scientist, or even a philosopher technically, when the debate was entitled, "Does God Exist?" he sometimes didn't fare as well because when it came to disproving god's existence, one needs a considerable amount of knowledge of cosmology, physics and biology.
One repeated argument Hitchens made, was that since modern humans had been around for at least 100,000 years, maybe 250,000, during which time they were dying of disease, defects, natural disasters, wars, usually living to be about 25-30 if lucky, and all that time "heaven" watches indifferently as all this misery and suffering is endured. Then suddenly about two or three thousand years ago, decides to intervene and reveal himself to "stupefied" Iron-age desert dwellers, and we are all asked to believe this was the work and plan of an infinitely intelligent being. How could any thinking person believe this, Hitchens asked his audience. What this argument sought to do was to establish how absurd it is to believe in a biblical god in light of the fact that we know our species evolved over many hundreds of thousands of years. It's similar to my Evolutionary Argument Against God, but not so formalized.
Hitchens never used formalized logic to make his arguments; his arguments were always explained. This can be a very effective method if one is, like Hitchens, a great story teller. I prefer to fight fire with fire, and enjoy using logical arguments against the believers - along with other methods like Hitchens' storytelling approach.
What God is Not Great sought to achieve was to make the belief in anything more than a deistic god completely absurd and untenable. I can credit Hitchens with making me an antitheist and catapulting me towards a more polemic and aggressive style of atheism, openly fed up with dealing with the "feeble-minded inventions" of those of religious faith. I'm glad that I got to see and meet him in person after his debate with Tariq Ramadan where he signed my copy of God is not Great. Watching his debates on YouTube makes me miss him and think of what he would be doing now, had he not succumb to his esophageal cancer.