The nature of logic

If I point to a man a say - he is short and then point to a women and say she is tall, but when you look at them you notice the man is taller than the women, you are fully justified to appeal to logic that short things cannot be taller than tall things.  Your observation renders my comment irrational (misapplication of words), unless I can add logically consist context like he is short for men, she is tall for women, and men are normally taller then women.  At that point, we have a fully logical explanation.

If however I said the man can be short and yet taller than the women at the same time because he is omnipotent, then we are back to an irrational statement and nothing more.

Logic is simply about the proper application of concepts to reality.  nothing can escape that application because it is merely a way to communicate abstract ideas and nothing more.  By definition then logic has to match reality, because that is the only thing that makes it useful - exactly like math (an even more pedantic language).

A person is irrational if they are either unable to recognize reality and thus cannot describe it properly with concepts or if they do not understand the words they are trying to use to describe reality.  Either of these two inabilities do not give rise to the possibility that reality changes magically (into gods) simply because someone cannot communicate.