This article will not try to demonstrate that God does, in fact, exist. It will not even attempt to provide a compelling argument for believing in God. This is not to say that there are many arguments for God's existence that are also logically fallacious. This is merely an attempt to show, in very few words, that these certain arguments against the existence of God are logically fallacious:
1. Man created God.
2. Therefore, God does not exist.
This is perhaps the most common logical fallacy: neuroscience and psychology have found that the human brain is configured such that man will believe in God given certain stimuli (see Freud, Totem and Taboo or The Future of an Illusion). Therefore, God must not exist.
The physiological evidence for this premise is not lacking, but I want to show that the conclusion does not follow from the premise. This argument is a flawless example of the genetic fallacy, a rule of logic purporting that it is fallacious to invalidate an argument because of the origins of the argument.
In other words, an argument is not weak because the history of how the arguer came to hold the argument is suspect. This does not mean that it is great to believe in God in the absence of evidence - however, it is to say that one commits a logical fallacy if she concludes that God does not exist because a man's physiology is the source of his belief in God.
So, even if I grant the fact that man first came to believe in God because of x (comfort in light of frightening circumstances, the desire for a powerful father, construction of sociological identity, etc.), it would be fallacious for me to conclude from this fact that he does not exist.
The fallacy applies because how I historically arrive at a belief has no bearing (apart from interest) on the substance of my argument. If you want to show that God does not exist, you must give a compelling argument against his existence in fact and against the substance of my argument. You cannot (according to logical rules) attempt to make an argument for God's existence weak by appealing to how I came to believe, instead of why.
In short, it is a fallacy of irrelevance. This is not to say that the conclusion that God does not exist is false. It is to say that this particular argument against his non-existence is invalid. If you wanted to have a substantial (non-fallacious) debate concerning God's existence, then you ought to discuss issues like God's nature and the problem of evil, whether the Big Bang needs an atemporal cause, whether there are objective moral values and duties if God does not exist, etc.
In language more conducive to other disciplines, discovering one's bias or predisposition is interesting and useful for other things. However, it deals with the arguer and not the argument.
Consider an analogous dialogue: "The death penalty is an immoral punishment," and "You only think that because you are from X." It might be true that many people from X are against the death penalty and that is strong reason why the protester is against the death penalty. But, it is easy to see that following the response, we are no closer to discovering the morality of the death penalty. In the same way, the psychology of religion is fascinating. Unfortunately, it says nothing about the religion's claims.
Does God exist? The predisposition of the brain cannot tell us - it is irrelevant to the subject at hand.