Inspired by Reppert's argument in C.S. Lewis's Dangerous Idea on pp. 57-58:
1. No belief is rationally inferred if it can be fully explained in terms of non-rational causes. (Premise)
2. If naturalism is true, then all beliefs can be fully explained in terms of non-rational causes. (Premise)
3. Hence, if naturalism is true, then no belief is rationally inferred. (From 1 and 2)
4. Beliefs can be rationally inferred. (Premise)
5. Therefore, naturalism is false. (From 3 and 4)
I modified Reppert's "materialism" to my own rendering of "naturalism." I also simplified (4) and (5).
The naturalist is likely to accept (1) and (4), but will almost certainly deny (2). After all, aren't our minds rational causes? In a word, yes. It's true that our minds are rational causes, but that's not quite what the argument is getting at. What the argument from reason stresses is that our minds are the result of some type of process. That process (e.g. evolution) either includes rational causes or strictly non-rational causes. It's the theist who says that evolution includes rational causes. It's the atheist who is committed to the view that only non-rational causes are at work in the formation of our minds.
With that said, why think our minds generally produce true beliefs if they are the mere result of non-rationality? If one wishes to bite the bullet and say our minds generally don't produce true beliefs, contrary to (3), then the belief that our minds are only the result of non-rationality is itself most likely not true!
This latter aspect is what Alvin Plantinga focuses on in his Evolutionary Argument Against Naturalism (EAAN). The claim isn't that evolution is false, but that naturalism is inconsistent with evolution and rational minds (Plantinga's term is "cognitive faculties"). Thus, the truth of evolution implies the falsity of naturalism.