The Future of an Illusion of 1927 is short and is regularly misquoted, because the key term is technical. An illusion, in Freud's definition, is not the same as an error and is not necessarily false. It is a belief whose motive force is the fulfilment of a wish, held with a disregard for its relation to reality. A middle class girl's belief that a prince will come and marry her is his example; it is an illusion, and it might happen.
Religious doctrines, on this account, are illusions in that precise sense. They answer the oldest, strongest and most urgent wishes of the species, and the psychological original is the child's relation to the father: helplessness before a power that both threatens and protects, resolved by love and obedience. Providence is that relation projected onto the universe. Freud does not claim to have shown the doctrines untrue, and says so explicitly; he claims to have shown what sustains belief in them independently of their truth.
What follows is a prediction rather than an argument, and it is the part that has aged least well. He expected that as science extended its reach, humanity would grow out of religion much as an individual grows out of the neurosis of childhood, and that an education to reality would replace consolation. A century later the prediction has failed in most of the world, which is a fact about the world that any account of religion, including a psychological one, now has to explain.