This was a guilty pleasure. Reading (or listening to) a non-fiction book by Baddiel is like having a conversation with a very smart and articulate person, who happens to have exactly the same views on everything as you do. I agreed with pretty much everything he said in Jews Don't Count, and it's the same story with this book.
It is very short, but could've been even shorter, since there is basically one idea: humanity desires God, mainly as a cure for mortality, and for other reasons as well, and if something is desired, but there's no evidence of its existence, then it follows that that something doesn't exist. A refutation of God's non-existence, according to Baddiel, would be someone earnestly believing that there is God, but wishing that there wasn't one. That would be a belief freed from desire (mind and senses purified etc.), and it would've at least put a chink into an atheist's armor, if not destroyed it completely. I'm not so sure about the last argument, as I can imagine some people believing in God, and yet being angry at him (there are plenty of reasons) with enough ferocity to wish him into the non-existence. But other than that, yes, sure, God is the projection of our fear of death and chaos. And, on top of everything, it doesn't work! As Baddiel points out, even at the peak of religiosity (let's say Europe in middle ages), people, devout believers as they were, still didn't want to die and considered death, their own and their loved ones', to be the ultimate calamity.
Baddiel sidesteps the questions such as "what would happen to our morality without religion", since his point is that God doesn't exist, period. And even if everyone admitting this would lead to a global catastrophe, that wouldn't change that basic fact. Even if to avoid this hypothetical catastrophe we will all have to pretend that there is God, God would still continue not to exist.
There is an interesting, if somewhat questionable, point about Judaism and Christianity, which he illustrates with the following anecdotes. When Baddiel's local rabbi invited him to light the menorah in the local synagogue on Hanukkah, Baddiel tried to get out of this by saying "unfortunately, I'm an atheist", to which the Rabbi responded "not a problem, so am I". On the other hand, Baddiel's partner Skinner, who is apparently a catholic, was genuinely afraid that him living in sin with his girlfriend would lead to him not receiving the communion, which in turn would lead to him going to hell. This, in Baddiel view, shows that Judaism is mainly about ritual, and God is somewhere at the fringes, whereas in most branches of Christianity there is a strong presence of God and the necessity to deal with him directly and possibly suffer the consequences. There may be something there (there is a ton of ritual in Judaism, and Jews certainly don't anthropomorphize their God and don't encourage direct interactions with him in the way Christians do), but I think it mainly has to do with the Reform nature of the religious Jews Baddiel is used to. An orthodox rabbi would never admit atheism and would be much more Christian-like in his preoccupation with God.