Belief in God is NOT Irrational
I will argue that belief in God is not irrational.
To show that belief in God is not irrational, I must show that there are reasons to believe in God.
(I would like to suggest, before moving on, that I am not required to definitively prove the existence of God. I need only show that belief is not irrational—that is, not without plausible reason.)
I will now present what will amount to a Cosmological Argument. I know you've all heard it, but bear with me.
Until recent cosmology suggested a beginning to time and space in the Big Bang, many people held that the universe was simply infinitely old. Suppose the state of the universe today is called S5. S5 could be explained in terms of the state of the universe yesterday, S4, and the laws of nature that acted on it. In turn, S4 could be explained by a previous state, S3, and so on. In an infinitely old universe there would be no first cause, so to speak, and so the very existence of the universe would be unexplained, as every cause is also an effect and there is no cause outside the set of effects. It's existence and the existence of the apparent laws of nature (physical laws) could be taken as a "brute fact".
However, it does not seem obvious that an actual infinity is possible. In fact, actual infinities lead to some very strange contradictions. If actual infinities do not exist in the world then the the series of states of the universe (S99, ..., S57, S56, ...) is not endless back in time, and there would be a first state—a state without a cause. And modern science does suggest the universe began to exist approximately 15 billion years ago.
The two points above are meant to demonstrate that it is not irrational to hold that the physical universe did, in fact, have a beginning. The alternative hypothesis—that it never had a beginning—is weaker, and possibly demonstrably false. And so, it is actually more rational to believe that the universe began.
Next, it is reasonable to wonder: if it began, why? Did it pop into existence from nothing? What caused it?
If you hold that it is impossible or unlikely that a universe would appear from the profoundest no-thing, you could reason as following:
The cause could not be a physical thing, because it created physical things. It created time, so the cause is non-temporal. It seems to have tremendous power and knowledge, and a will, and it cannot be mechanical, or comprised of parts. It would appear, then, that this cause is some sort of mind.
We are therefore above asked to consider two options: the universe just began without explanation or reason, or the universe began with explanation and reason. It is at least not more reasonable to assert that it simply began, from nothing and by nothing. That would run contrary to every single observation and experience of the world and the universe that any individual or science as a whole has or ever could make. So it is at least as reasonable to hold that time and space were created—and, if so, by a being that is non-spatial and non-temporal.
1) I think that I have shown that a) it is perfectly reason to believe the universe began and b) it is also reasonable to hold that a universe cannot appear from nothing.
2) I think that I have also shown that given a) and b) it is reasonable to figure that the cause of the universe is non-temporal and non-spatial.
From here, I recognize that there is room to discuss the coherence of the idea of a non-spatial, non-temporal mind, and of the nature of causality and time at or "before" the Big Bang, etc.
Those are complex issues that must be rigorously treated, with intricate arguments on both sides, and I will not treat them here, nor do I have to for my purpose.