Okay, let me try it this way.
Rational people can have irrational beliefs. This doesn't make them irrational. Really, almost everyone has them, to some degree. However, someone who has a functioning brain, who applies their logic and reason every day, has to compartmentalize their beliefs. If you can't apply your logic and reason to something, then it gets stored away in it's own category in order for that person to continue believing it.
This obviously makes it very unlikely that the person will regularly reflect on this belief.
For instance, ghosts. Many perfectly rational and intelligent people believe in ghosts, but the way they think about ghosts is very different to how they think about the average day to day events. They pay lip service to the belief and treat it like it's a normal belief, but they rarely think about it in any meaningful way. They consider what they will eat, how they will do their job, what they will spend their money on, and wonder how their car works, but when it comes to ghosts, they simply believe without that kind of habitual pondering. It's like a 'no think zone', if that makes sense.
That's fine. However, for a topic as personal and defining as a God, some people can't keep it in that no think zone, they have to justify it and make a case for it, and you can't really do it, so any argument formed has to be illogical, just made to sound logical.
