The problem is the person who claims that he can believe only what results from reason, i. e., the application of logic. Why is that a problem? Well, how does one verify that principle, that knowledge can only come from reason? If you use reason to demonstrate it (by which I do not mean that is possible), then you have already violated your principle by using the fallacy of circular reasoning. Reason must be verified before it can be applied. On the other hand, if you use something other than reason (not that I can imagine what that might be), then you have violated your own principle. Either way, you can only falsify the principle, not prove it.
Therefore, bald reason cannot be the foundation of knowledge. By its own principles, that conclusion is unavoidable.
On the other hand, let me return to the assertions with which I started, i. e., that logic is part of the nature of God, and thereby of men, because we are made in His image.
On that basis, I have a foundation for reason that is neither circular nor self-refuting. That is the difference between the Christian and the rationalist atheist. Not that one is rational while the other is not. But rather that the one has a foundation for his reason, while the other does not.
This is simply what is asserted by God in the Bible: "The fear of the LORD is the beginning of knowledge" (Proverbs 1:7). It is with this sure foundation that all reason is possible.
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