Assuming that one comes to belief by way of reason (as you say where I bolded) but surely that is the exception if/when it ever happens. Reason is most often cited as why atheists come to their disbelief too. But those who actually believe propositions expressed in the Bible as a kind of surrender to reason have more in common with the atheist than with people of faith. It isn’t that either the atheist or the rationalist believer has miscalculated. That both rely most heavily on intellect mark them as true brothers and both make the same mistake.
“Self refuting”? How convenient.