Many atheists consider themselves "rationalists", and defenders of rationality. But it is evidence of their irrationality the fact that they don't understand that the basic premises of the impersonalistic naturalistic worldview makes "rationality" almost impossible, since rarionality requires at least two conditions:
2-Free will (in order to respect the laws of logic and evidence, and freely choose what's rational over what's irrational)
Both person-relative features are in variance with the impersonalistic fabric of reality essential to naturalism, and in fact provide good evidence for theism.
Moreover, contemporary naturalists are committed to evolutionary theory and this theory itself (independently of the two features mentioned above) support skepticism regarding our rationality and cognitive faculties. As Charles Darwin himself realized: "With me, the horrid doubt always arises whether the convictions of man's mind, which has been developed from the mind of the lower animals, are of any value or at all trustworthy. Would any one trust in the convictions of a monkey's mind, if there are any convictions in such a mind?" (Darwin's letter to William Graham, July 3rd, 1881,)
As philosopher Alvin Plantinga, has argued in this article: "Now what evolution tells us (supposing it tells us the truth) is that our behavior, (per-haps more exactly the behavior of our ancestors) is adaptive; since the members of our species have survived and reproduced, the behavior of our ancestors was conducive, in their environment, to survival and reproduction. Therefore the neurophysiology that caused that behavior was also adaptive; we can sensibly suppose that it is still adaptive. What evolution tells us, therefore, is that our kind of neurophysiology promotes or causes adaptive behavior, the kind of behavior that issues in survival and reproduction.
Now this same neurophysiology, according to the materialist, also causes belief. But while natural selection rewards adaptive behavior (rewards it with survival and repro-duction) and penalizes maladaptive behavior, it doesn’t, as such, care a fig about true belief. As Francis Crick, the co-discoverer of the genetic code, writes in The Astonishing Hypothesis, “Our highly developed brains, after all, were not evolved under the pressure of discovering scientific truth, but only to enable us to be clever enough to survive and leave descendents.
Since natural selection favors useful beliefs (for survival and reproduction) and not true beliefs per se (specially not true beliefs about sophisticated and highly abstract and theoretical topics not directly or indirectly related to survival and reproduction, like mathematics or quantum mechanics), there is not reason to think our cognitive faculties are aimed to the truth (instead of simply being pragmatically useful for crude survival purposes).
Serious and first-rate naturalistic thinkers have realized the problem of rationality in a naturalistic worldview. Leading naturalistic-atheistic philosopher Thomas Nagel, in his book The Last Word, wrote: "The problem then will be not how, if we engage in it, reason can be valid, but how, if it is universally valid, we can engage in it... Probably the most popular nonsubjectivistic answer nowadays is an evolutionary naturalism: We can reason in these ways because it is a consequence of a more primitive capacity of beliefs formation that had survival value during the period when the human brain was evolving. This explanation has always seemed to me to be laughably inadequate... The other well-known answer is the religious one. The universe is intelligible to us because it and our minds were made for each other" (p.75)
What Nagel calls the "religious" option, is more properly called the "theistic" option. In theism, the universe is intelligible because, both the universe and human beings, were created by a rational God. Therefore, it is not surprising that our limited and imperfect cognitive faculties (reason, logic, memories, etc.) FIT the real world in more or less accurate ways. In fact, the latter is precisely what we would expect IF theism were true, because in theism we're created in God's image (i.e. sharing, in a limited form, some of God's superlative personalistic attributes, like rationality, capability to knowledge, moral agency, free will, etc.).
But in naturalism, there is not reason to think that our beliefs fit the real world, instead of being only useful for survival and reproduction, specially if the Darwinian evolutionary theory about the mind is true. As naturalistic philosopher of science and biology, and hard-core defender of Darwinism, Alex Rosenberg recognizes "there is lots of evidence that natural selection is not very good at picking out true beliefs, especially scientific ones. Natural selection shaped our brain to seek stories with plots. The result was, as we have been arguing since Chapter 1, the greatest impediment to finding the truth about reality. The difficulty that even atheists have understanding and accepting the right answers to the persistent questions shows how pervasively natural selection has obstructed true beliefs about reality" (The Atheist's Guide to Reality . p.110)
Note carefully, the argument is NOT that natural selection favors only false beliefs. Rather, the argument (at least as developed by Plantinga) is that natural selection is INDIFFERENT to the truth-value of beliefs, provided these beliefs are useful for survival and reproduction (In Rosenberg's view, the problem is even worst because for him natural selection promotes false beliefs and tends to prevent reaching true beliefs. If Rosenberg is right, then it is very likely that most of the beliefs favored by natural selection be false. But let us be more charitable to naturalism).
And since the number of false beliefs which are pragmatically useful is greater than the number of true beliefs, is obvious that natural selection cannot be very good to choose the truth over falsehood.
This implies skepticism regarding our rationality and cognitive faculties. Philosopher Willliam Lane Craig has summarized this argument here:
As naturalist Richard Dawkins strongly argues: "But doesn't a truly scientific, mechanistic view of the nervous system make nonsense of the very idea of responsibility, whether diminished or not? Any crime, however heinous, is in principle to be blamed on antecedent conditions acting through the accused's physiology, heredity and environment. Don't judicial hearings to decide questions of blame or diminished responsibility make as little sense for a faulty man as for a Fawlty car? Why is it that we humans find it almost impossible to accept such conclusions? Why do we vent such visceral hatred on child murderers, or on thuggish vandals, when we should simply regard them as faulty units that need fixing or replacing? Presumably because mental constructs like blame and responsibility, indeed evil and good, are built into our brains by millennia of Darwinian evolution."
Dawkins clearly perceives the problem of "responsability" and freedom of will (and other "mental constructs" like the "good" or the "evil"), which don't exist in reality, only in our brains. In Dawkins' naturalistic, impersonalistic worldview, we're mere automata governed by physical laws operating on our "physiology, heredity and enviroment".
As consequence, Dawkins' choice of accepting naturalism over theism is ALSO the product of deterministic physical laws, not of Dawkins' free decision to be rational. (Note the irrationalistic implication of Dawkins' own position to favor "reason").
Scientific naturalism is, ultimately, destructive of rationality. It appeals to "reason", "science" and "logic", but its basic impersonalistic premises undercut the possibility that such things do exist.
As consequence, scientific naturalism is essentially and intrinsically irrational.