Reasoning requires thinking about what sorts of things do and do not make sense. This thinking may correspond, much of the time, with the "laws of logic," but it doesn't "require" that these laws have some kind of avatar in our heads which is part of the chain of events causing the correct conclusion to come out. (That's what "requires" seems to mean generally, as in "the car's engine requires a working carburetor"; I understand that as meaning "the carburetor's action is part of the chain of events causing the engine to work.")
The thesis of philosophical naturalism is that physical events in the brain cause mental events; that with larger and more complex brains, a further range of mental events is possible, including not just feeling pleasure and pain but considering what's true and what's false; and that with natural selection, the conclusions about what's true and what's false become more and more reliable. Obviously, you can dispute any of these premises; but you have not really made an argument yet for why, taken together, they are ultimately self-contradictory.