By Lewis's reckoning, the fundamental distinction is between Naturalists, who believe the world operates entirely by material phenomena, and Supernaturalists, who believe in "something" that exists outside of Nature, has to do with the nature of Reason. The reason Naturalism fails is that it cannot account for the rise and existence of human consciousness and will. That a mechanistic system could result in an intelligence so decidedly un-mechanistic seems to Lewis a fatal chink in the Naturalist's armor.
The logic used is circuitous and frankly baffling, hinging as it does on such split hairs as the use of the word because and Cause and Effect vs. Ground and Consequent. But the nub of the argument is thus:
The Naturalist might say, 'Well, perhaps we cannot exactly see--not yet--how natural selection would turn sub-rational mental behaviour into inferences that reach truth. But we are certain that this in fact has happened. For natural selection is bound to preserve and increase useful behaviour. And we also find that our habits of inference are in fact useful. And if they are useful they must reach truth'. But notice what we are doing. Inference itself is on trial: that is, the Naturalist has given an account of what we thought to be our inferences which suggests that they are not real insights at all. We, and he, want to be reassured. And the reassurance turns out to be one more inference (if useful, then true)--as if this inference were not, once we accept his evolutionary picture,  under the same suspicion as all the rest. If the value of our reasoning is in doubt, you cannot try to establish it by reasoning.
This rests on two assertions:
1. The Naturalist position here presented casts doubt on the reliability of human reason.
2. With reason in doubt, the Naturalist position cannot be made (reason can't be used to prove that it can't be used).
What we have is a false dichotomy, (similar in fashion to Lewis's other, more famous Lord, Liar, or Lunatic trichotomy on the question of Christ's divinity), true on its own terms but falling apart when its assumptions are questioned. Reason is not blindly championed by Naturalists--the scientific method exists after all to thwart individual bias and human error. That it should be doubted then is no great surprise.
That human fallibility should be such an affront to Lewis's sensibility begs the question: if we cannot trust our senses to give us a reasonably accurate picture of the world, the position Lewis thinks is a consequence of Naturalism, what should we trust?
Lewis was, of course, not a Naturalist, and doesn't need to answer this. But his own position, after several wearisome pages of attacking Naturalism, qualifies less as an argument than magical thinking (emphasis mine):
But the Theist need not, and does not, grant these terms. He is not committed to the view that reason is a comparatively recent development moulded by a process of selection which can select only the biologically useful. For him, reason--the reason of God--is older than Nature, and from it the orderliness of Nature, which alone enables us to know her, is derived. For him, the human mind in the act of knowing is illuminated by the Divine reason. It is set free, in the measure required, from the huge nexus of non-rational causation; free from this to be determined by the truth known. And the preliminary processes within Nature which led up to this liberation, if there were any, were designed to do so.
In other words, God did it and that's all there is to it.
Frankly, neither explanation is completely satisfying. The materialist must maintain his own faith in science to show by experiment that consciousness--to say nothing of life itself--can arise by organic means.
But at least it articulates some sort of process by which consciousness could arise and is honest about the holes in its knowledge. Explaining everything by recourse to a force that just happens to be all-powerful and invisible, explains nothing. It pulls the answer out of thin air and leaves it to fall to the ground. It waves away inconvenient questions (if God can exist beyond the Universe, what's to stop something else from existing beyond God? If it's beyond our capacity to know, then why speculate on his intents at all?) while shrugging the shoulders.
To close this entry, I point out Lewis unintentionally demonstrates the ridiculousness of his position by summarizing with a quote by J.B.S. Haldane:
If my mental processes are determined wholly by the motions of atoms in my brain, I have no reason to suppose that my beliefs are true . . . and hence I have no reason for supposing my brain to be composed of atoms.
This recalls the opening chapter of The Men Who Stare at Goats, in which a character similarly conflates particle operation and human endeavor:
Am I ready? he thinks. Yes, I am ready.
He stands up, moves out from behind his desk, and begins to walk.
I mean, he thinks, what is the atom mostly made up of anyway? Space!
He quickens his pace.
What am I mostly made up of? he thinks. Atoms!
He is almost at a jog now.
What is the wall mostly made up of? he thinks. Atoms! All I have to do is merge the spaces. The wall is an illusion. What is destiny? Am I destined to stay in this room? Ha, no!
Then General Stubblebine bangs his nose hard on the wall of his office.