No, your reasoning is faulty because Islam is based on the Koran which is in itself irrational. It has so many contradictions that it stands for nothing and everything, whatever you want it stand for. You can't justify an irrational ideology that is based on irrational, contradictory rules of morality. You are using circular logic.
There is no circular reasoning here. You are quite reasonable in saying they are illogical, based on your standards. You can even say that their standards are wrong and you are welcome to try to convince them. But you can't say that they are illogical based on their standards and their standards are what they use to make decisions.