The evolutionary argument against atheism (naturalism*, specifically) challenges the compatibility of naturalism with the reliability of human cognitive faculties, particularly those involved in forming beliefs about the world.
The argument is often associated with Alvin Plantinga, a contemporary American philosopher. The basic idea is as follows:
Evolutionary Naturalism: Assume that naturalism is true and that human cognitive faculties have evolved solely through naturalistic processes like natural selection.
Truth-tracking: For our cognitive faculties to be reliable, they must be aimed at truth. In other words, if our cognitive faculties are functioning properly, they should generally produce true beliefs about the world.
Survival Fitness: According to the theory of evolution, the primary driving force for the development of our cognitive faculties is not necessarily truth-tracking, but rather survival fitness. The idea is that beliefs and cognitive processes that enhance survival and reproduction would be selected for, regardless of whether those beliefs are true.
No Guarantee of Truth: Given the above, there is no reason to assume that the beliefs produced by our cognitive faculties under naturalistic evolution are necessarily true. They might simply be beliefs that increase our chances of survival, even if those beliefs are not aligned with the actual truth.
Undermining Confidence: If our cognitive faculties are not reliably aimed at truth but are primarily geared toward survival, it undermines our confidence in the truth of our beliefs, including the belief in naturalism itself. If naturalism is accepted, it implies that our cognitive faculties are reliable, but the argument suggests that naturalism undermines the very reliability of those faculties.
In summary, the evolutionary argument against naturalism raises questions about the reliability of human cognition under the assumption of naturalistic evolution. It challenges whether a naturalistic worldview can provide a secure foundation for believing in the reliability of our cognitive processes and, by extension, the truth of our beliefs (including evolution).
* The view that only natural entities and processes exist, and there is no need for supernatural or non-natural explanations. It's possible to be an atheist but believe in supernatural entities; Plato's forms, let's say.