existence needs no proof. That is why it is an axiom. Existence is self evident and you either accept it reject it but as soon as you ask for proof you are presupposing that something exists. Don’t you know that you exist?
Logic rests on existence and the law of identity. Once again existence needs no proof it is its own proof. I will go further and say that existence needs no explanation. It just is and always has been and always will be. It is self evident.
Belief based on mysticism is irrational and there is no way around that fact. That is not my opinion that is simple logic. Logic is not man made. It is a process and the only process available to man by his nature to know anything.
If your neighbor tells you that he was abducted by aliens last night and they performed medical experiments but that they left no physical evidence of their abduction and you believe him that is irrational. That is faith. If you believe the holy spirit is showing you some new insight in the bible that is irrational. If you accept that Cain killed Abel and was punished by God that is irrational.
So the conflict is caused because people of faith want to demand the unearned status of rationality. They want others to abandon reason and join them in saying that faith in the supernatural is reason and it is that simple. Live by faith if you want to but don’t call it reason.
Prove that statement or concede that you can say the same thing about anything else. There is no third choice. In addition we accept the laws of contradiction, excluded middle and Euclid's axioms without any proof. Thus, EVERY single worldview accepts certain matters purely on faith without any rationale "proof".
Why is that irrational as opposed to improbable? Please define your terms if you are going to use them outside thier traditional meanings. Or are you saying anything improbable is irrational?