Eli Bendersky's website The central argument against god in this book, that also addresses the number 1 claim of religious people as to god's existence, is (p.157):
1) One of the greatest challenges to the human intellect, over the centuries, has been to explain how the complex, improbable appearance of design in the universe arises.
2) The natural temptation is to attribute the appearance of design to actual design itself. In the case of a man-made artifact such as a watch, the designer really was an intelligent engineer. It is tempting to apply the same logic to an eye or a wing, a spider or a person.
3) The temptation is a false one, because the designer hypothesis immediately raises the larger problem of who designed the designer. The whole problem we started out with was the problem of explaining statistical improbability. It is obviously no solution to postulate something even more improbable.
Dawkins also spends considerable time trying to understand why religion is needed. He raises some interesting hypotheses. A couple of examples:
* Religion is a by product, a mis-firing of some other psychological property of our brains. The best example for this property seems to be found in children, who often believe unquestioningly what their elders tell them. Additionally, children often have "imaginary friends" in whom they believe ardently, refusing all attempts to dispute them. The child's claim that "even if you say he isn't there, I feel it, so it's true" should sound familiar to anyone who had the chance to hear some religious people explaining their faith.
* "Cargo cults" as an example of a recent, documented spring-up of religion. Google it, it's a great story to learn from.
* People don't make the distinction between believing in god and believing in belief: the belief that it is desirable to believe, even if the belief itself is false. Quote (p.352): "I think we all know people who enjoy the idea of religious faith, and resent attacks on it, while reluctantly admitting that they don't have it themselves".
To conclude, I will mention that Dawkins notes somewhere in the beginning that he wants this book "to convert believers into atheism". I'm sure he doesn't believe it will happen himself. This book is too offensive to religion, acrid and sarcastic on many occasions - all of which sounds good to an atheist (or perhaps an agnostic), but a religious person will just find it repulsive. What this book can do, however, is "adjust some bolts" in the mind of an atheist who doubts for a moment. Because no a reasonable, logical human being will stay indifferent to it - for such people it is a true pleasure to read. The book addresses so many important topics, in such a lucid and succinct way, that it is very difficult to summarize it in a review. Just read it.