You're confusing the map for the territory. Rationality is something that makes sense for us. That need not apply to nature. It's misplaced to say that nature is rational. Nature just is.
So nature cannot be irrational. For instance: we had the very logical Newtonian mechanics. But Mercury's orbit did not make sense. Later on Einstein saw another layer of logic that put both Newton and Mercury in more context, and now both make sense again.
When we see things now that make no sense, it indicates faults in our mental models, not in the things.
In the context of a person behaving or thinking "irrationally": their brain is just atoms and chemicals. It has to work right. If their behaviour and thoughts do not line up to reality, that's a feature of said brain.
Perhaps the irrationality is due to the brain giving too much weight to certain factors, or perhaps they are in fact behaving perfectly logically given what they know and you don't. Perhaps its workings can be improved in software, or in the next hardware generation.
But there's no spooky mechanism that can't in principle be modelled and implemented in a different architecture, ie, transistors.
