Freud said that the worship of God and belief in God is not about whether there
is such a being or not but about comforting ourselves - it is an attempt at
wish-fulfilment. This the Projection Theory.
Observation shows that what people think of each other and God stems largely from how they think of themselves. As God is not going to correct you like your neighbour will when you get the wrong the projection would be far worse there. Then there is the doctrine of Christianity that your neighbour is the image of God and God shows himself in every person. That is asking for projection.
Christians say that Freud's view presumes that there is no God whereas the right thing to do is to look at the evidence first and then make up one's mind. Christians reject the thought "The worship of God and belief in him is us trying to comfort ourselves with this notion (it's a wish projection) which means the notion is false."
The reply is that the Projection Theory so far is not necessarily saying there is no God. It is only addressing the psychological attractions of worship and belief. Even if there is a God, you may still be worshipping a God that is your own invention or projection.
Freud also said that God was based on your own father. You invent a father in the Heavens modelled on your own father.
I would prefer if he had said that God was a projection modelled on your father or mother or both. Though God is described as male, many Christians go on as if they were safe in God's arms and womb and are attracted by the feminine emotions they attribute to God.
Freud did however notice that religious people acted the same way as neurotics. He saw religious ritualism as showing that religion was a form of obsessional neurosis. I would point out that all who claim to be Christians have an obsessive side with regard to religious texts. They pick out favourite ones and centre their faith on them and read too much into them. For one to look at, "You are Peter and on this rock I will build my church" and work out the papacy from that is definitely abnormal. Peter was only the support of the Church not its head and even Peter left no papers or rules about a successor.
Christians say that Freud's theory was just his prejudice because he never psychoanalysed any believer in God and found the psychological causes. Apparently no such psychoanalysis has ever been attempted.
Freud became a psychoanalyst just because he was an atheist so it was more than just a prejudice. All the psychoanalysis he undertook confirmed him in his atheism. He did not need to attempt psychoanalysis specifically to find out the causes of belief in God. Indeed why would he have done that and discredited his profession? He was against religion and considered it dangerous but he didn't want to go so far as to treat everybody who believes as being on a par with manic depressives or schizophrenics.
Christians say the projection theory cuts both ways. If Christians for example might be kidding themselves that there is a God because they want a father figure atheists could be kidding themselves that there is no God for they don't want to believe that they have to answer for their actions to a deity. They want rid of moral constraints. Perhaps some atheists had bad fathers and hate God because they see God as a father figure. Certainly it may be unkind for religion to make out that God is father.
Fair enough. But it takes a stronger projection to imagine God will punish your enemies, forgive your sins and grant you a Heaven than it does to deny those things.
Some religious masochists and sadists like a God who condemns them and others and who forbids them from having an enjoyable life. False humility is rife in religion. People punish themselves to get attention. As they weep in sackcloth and ashes, they are secretly looking down their noses at those who are not doing that.
It is shocking how evil people, devout Mafia Dons come to mind, expect divine punishment and God's harsh rules to apply to others and are confident that he forgives them or has a plan for them. To say that God has a plan to turn evil into the seed of good is to say he likely has a plan to get you forgiven by him even if you are estranged now. Mafia Dons who are less confident still consider it worth the risk.
Christians say that the reason we desire God is because there is a God. This when studied carefully is an admission that Freud was right.
An excellent proof that Freud was right is from prayer. People feel good about praying for prayer is based on trust in God and it feeds that sense of trust. Trust is a feeling that the bad will pass and better days will come. But evil by definition is uncontrollable. If God allows evil for a greater purpose as religion says, it follows that he may have to put up with evil forever. But they are too sure that the particular evil they are trying to combat prayerfully will go away. This amounts to watering it down in your own head to feel better.
Also if one prays for something and doesn't get it or get a good alternative, the failure will be blamed not on God but on the person's alleged lack of faith. Jesus said that prayers made without faith are not replied to by God. This is like how psychics also blame their failures on lack of faith. The person shows a wish to distort the evidence that prayer does nothing special. If prayer is the basis of his faith in God, then his faith is a projection of his own desires.
Freud argued that as being neurotic too often meant being religious that being religious was an illness and a neurosis. Christians say that if it is true neurotic people are usually religious that does not prove religion was the cause. They say that religion stirs up passion and zeal which is why people with neurosis are drawn to it. But you will find this passion and zeal only in a few Churches and as soon as the service is over that is the end of the passion and zeal. Neurotics have been devoted mostly to dull and boring religion. So the conclusion is unavoidable - being religious and devoted to God is a symptom of mental illness.
The believers in God complain that there is no proof or good evidence for Freud's theory. But is there any for their insistence that he is wrong? No.
We must accept Freud's theory of God as being wish fulfilment as being a good one and of being better than any alternative view.