"Why do religions exist?"
Religions exist due to multiple motives.
A person will abandon their initial religion if they judge that that religion does not adequately fulfill their motive(s), and/or if they judge that a different religion fulfills them significantly better. Those motives include the following:
1. One honest and innocent motive is that a person has an intuitive sense that there exists one or more higher powers who have greater knowledge and wisdom than any human; or in some cases, that there exists one or more persons who have greater knowledge and wisdom than anyone else. And so they believe in and follow the teachings of that being(s), be it divine or human. This particular motive motivates me personally.
2. A second honest and innocent motive is the mysticism motive.
In this motive, a person has an intuitive sense that there exists something supernatural that is beyond human control, and such people desire to get closer to that supernatural thing and to experience it. This is a second motive that motivates me personally.
3. In contrast to the honest and innocent motives, there is the dominance motive,
in which a person adheres to a religion because the religion provides them an excuse for satisfying their depraved dominance-indulging desires, and can give them a delusional sense of autotheism (self-godhood) while doing so. In those cases, psychopaths have written scriptures in the name of a god- scriptures which advocate brutal dominance-assertion against babies and children (foreskin amputation), disobedient or resistant children, adulterers, apostates, "blasphemers", and others. Many of the laws in the Torah, mostly execution laws, were written by one or more of such dominance-craving psychopaths. In addition to those dominance-indulging actions, a religion may also provide the opportunity to indulge in dominance-asserting threats upon other people- a threat to believe in the religion or else face some imaginary horrible punishment in an afterlife. Christianity and Islam both provide people with that threat opportunity. The psychological purpose of dominance-asserting aggressive behaviors is to fuel one's own delusional sense that oneself possesses one or more other individuals.
4. There is also another depraved motive, which is even more depraved than the previous one
(though it has some overlap with the previous motive):
It is the cultist mentality motive, in which a person has a desire to delusionally feel as if oneself encompasses other people, and to have the resulting delusion that other people need oneself to persuade them of something or even to force something upon them, or else the targetted people will not be satisfied in life, or they will die, or they will suffer some other bad fate. That "sense of encompassing" is a mixture of two component sensations, namely dominance (as in the previously-mentioned motive) and antagonistic expansion, and it often involves an autotheistic feeling. The core doctrine of Christianity (that people need to accept a specific person as their personal savior, or else suffer eternal torture) readily "plugs in" to that pre-existing desire, such that the self-proclaimed savior-person becomes psychologically associated with oneself.