Suppose that a caricatured rationalist atheist (R) and a caricatured devout Catholic (C) have a discussion about the existence of God. Let’s say R defends his position by some argument against God’s existence (e.g. the existence of evil), and let’s further assume that C rebuts R’s argument to the point where even R acknowledges that his defence fails. If R does not change his mind, is he being unreasonable? Conversely, let’s assume that C defends his position by some argument for God’s existence (e.g. the argument from contingency), and let’s further assume that R rebuts C’s argument to the point where even C acknowledges that his defence fails. If C does not change his mind, is he being unreasonable? Or, let’s take an even more extreme scenario: let’s assume that before R or C even present their arguments, both individuals try to get their counterparty to agree that he will abandon his position should his argument be defeated, to which both parties reply that no, even if all their arguments for believing their position are defeated, they will continue to hold that position. Are R and C both being unreasonable?
Conventional wisdom would suggest that both R and C are being equally unreasonable in the above: reasonable people change their mind when their arguments are defeated, or so custom dictates. A more sophisticated person might note that R’s and C’s apparently unreasonable behaviour might belie a less recalcitrant internal set of attitudes, and as such they might in fact think reasonably even if they are acting unreasonably. A yet more sophisticated person might note that, in line with something like the Duhem–Quine thesis, R and C have actually gone outside the realm of “reasonableness” altogether, since something like “belief in God” is a core position that will inform one’s entire worldview and as such it is not really amenable to persuasion. But I want to suggest something different: the only person who could possibly be accused of unreasonableness or need defending is R. C is entirely justified unless one begs the question.
Note that for R, his ability to rationally defend his positions is critical to his reasonableness. For (at least the caricature of) a rationalist, man truly is the measure of all things, and so he must either be able to defend his position directly or be able to defend an appeal to authority for his position. Critically, however, the second option will by his own standards be subject to an infinite regress: if he cites a psychology finding, for instance, we might ask him to justify his belief in psychology (at which point we could direct him to the replication crisis); if he wants to defend his claim against the replication crisis, he will need to appeal-to-authority to statisticians or philosophers of science, at which point we might point him to rebuttals of them; and so on. R will as an obvious empirical fact not be able to justify the full epistemic chain, and what’s worse this will prevent him from having any proper justification in appealing to authority. Unless he is able to defend his own position to his own satisfaction, he will be forced to make a move that he himself considers unreasonable. His argument will straightforwardly lack validity.
For C, however, no such dilemma ever obtains. Our devout Catholic C holds a position first and foremost because they believe that the Church possesses, through the grace of God and the work of the Holy Spirit, the unique gift of proclaiming truth to the world, and so what the Church teaches as dogma is therefore correct. C not only has personal experience of the Holy Spirit; they most likely also have experiences of the Church’s ability to give valid and strong arguments for its own positions (e.g. on the existence of God, one might look to the aforementioned argument from contingency, or the Ontological Argument, etc.). Hence, C has no empirical grounds to doubt the claim that the Church, by divine grace, does in fact teach the truth, and so if C is defeated in an argument, the most reasonable belief that C could hold is that he made an error in reasoning, not that his position was incorrect. God, not man, is the measure of all things, and self-evidently C’s personal fumblings in argumentation do not indict God. Hence, his appeal to authority will be entirely valid. There is no infinite regress. C has made no leaps of faith aside from his original leap of faith, and he can justify that in good part within his system by means of rational arguments that even his interlocutors must accept as ostensibly valid.
In other words, the only way we could come to the conclusion that R and C are both being unreasonable is if we presuppose the truth of rationalism—which is clearly not a legitimate move in a debate over whether rationalism is true (and a debate over the existence of the Christian God is precisely such a debate). R and C will both ultimately be forced to make appeals to authority in defending their beliefs, but only one of them is in any real sense justified in doing so. If caricatured rationalists are disappointed by the insubstantiality of their own appeals, perhaps they should consider a philosophy that vindicates appeals to authority more rigorously.
 Note: “dogma” is a specific technical term in Catholicism, denoting a certain set of beliefs that have been divinely revealed (e.g. belief in the Trinity, the Immaculate Conception, etc.). Many beliefs held by Catholics—indeed, many beliefs advocated by the Church—are not dogma and therefore are not guaranteed of infallibility. So to be convinced of the Church’s infallibility in teaching dogma is not to be convinced that, for instance, the Pope would never accidentally misspell someone’s name. For a broader dissection, see here: https://www.catholic.com/magazine/print-edition/dogma
 Note: this diatribe is intended only against caricatured rationalists. While as an empirical point most rationalists do appear to act like caricatured rationalists, it is obviously false that the above succeeds in attacking any sophisticated doctrine.