Psychoanalysis is neutral with respect to the question of God's existence. The projection theory is an autonomous argument and was first developed not by Freud, but by Ludwig von Feuerbach, a philosopher who was avidly read by the young Freud. According to psychoanalysis, the child has a desire to kill his father and to lie with his mother. Freud called this the 'Oedipus complex'. The argument can be made that, due to this complex, we have an unconscious desire to kill God, the father figure.
Atheism is thus merely Oedipal wish fulfillment.
In many prominent atheists in history, we see a strong antipathy toward their fathers. Voltaire was not an atheist, but he rejected the idea of a personal god. Diderot, likewise, was a profound atheist. Freud himself observed that young people tend to lose their religious faith as soon as they lose the authority of their earthly fathers. The father is present, but he is weak, cowardly, unworthy of respect.