Sometimes the shortest answers to questions are the best, because they provide a framework for a lifetime of study, rather than attempt to present a detailed answer to a small part of a question.
In a recent (January 2013) edition of Philosophie, Charles Pepin, a French philosopher, was given just a few paragraphs to answer the question 'Why do people believe in God?'
He set out three options:
1. God exists, and his existence can be proved. If so, he makes the point that there is no longer any need to 'believe' in God; one simply knows about him.
2. God does not exist, but people want to believe in him anyway in order to make sense of their lives or for consolation. This is the approach taken by Nietzsche, Freud and Marx.
3. We don't known if God exists. This he regards as the most interesting option, because it enables us to engage with our own uncertainty.
Taking this framework as a starting point, one can explore the whole range of arguments about the existence and nature of God.
Most courses in Philosophy of Religion include classic arguments by Aquinas and Anselm. But one of the main question marks hanging over these and all similar arguments is whether what is proved actually corresponds to what most relievers call God. The arguments are all interesting in themselves, and may point to a form of deism, but they are seldom regarded as sufficient in themselves to decide the matter of god's existence. Indeed, as is often pointed out, they were never regarded as a substitute for faith, merely a way ifs engaging the intellect in what was already believed.
I am also aware, whenever I read Aquinas, that he held that God could not be an existing thing in any normal sense of that word. God did not have existence, but was pure essence. That, in itself, says a great deal about the arguments and what they were and were not intended by Aquinas to achieve.
The second approach, regarded generally as a disproof of the validity of religion, shows the human need that religion addresses. But there's a gap in the logic here. We all engage with life in a way that is determined by our personal needs and interests. We encounter everything 'as'. We are never simply objective observers. We create value systems and images to enable us to make sense of life. If god is one such human creation, it explains but does not automatically devalue religion. In the name of humanism, it is all too easy to assume that human reason alone will sort out all problems. We know that is naive. Reason is, and has always been, the slave of the passions, as Hume said. God, and belief in god, is more a matter of the passions than the reason.
Then the third approach is that of a healthy agnosticism - engaging with the mystery of experienced life and its values, without claiming to have any simply answers. That, as I have always argued, is the most rational approach to religion, as well as the one that enables the whole issue to be considered in ways that are meanIngful to both believer and non-believer.
But, in my view, the prior question concerns the meaning of the word 'god'. Unless that is tackled, and we are in broad agreement about what we are talking about, no progress on any of the three approaches will be satisfactory. Without such agreement, we are stuck with a dialogue of the deaf; neither side believing that the other can be quite as naive as they appear, and getting increasingly frustrated when reason fails to change minds.