In this piece he makes a number of claims that are either flatly false, or contradict what we know, or are given without any justification at all. Why he thinks this kind of pompous tripe will convince anyone is beyond me. Maybe, in their jobs, neurosurgeons get accustomed to making pronouncements that everyone else accepts without questioning.
I lack the time to do a complete fisking here, but I'll mention a few of his bogus claims.
1. "The accepted definition of reason is simple and straightforward: it is the power to think abstractly, without concrete particulars."
Whenever Egnor talks about something being "accepted" or "simple and straightforward", you can be pretty sure that the opposite is the case. Anyone who wants to check Egnor's claim can just go to the Oxford English Dictionary and type in "reason". There are three senses for the word, two as a noun and one as a verb. The uses as a noun include 17 different subdefinitions and another 15 or so different usages in phrases. The uses as a verb include 8 different subdefinitions. The word "abstract" appears nowhere in any of these subdefinitions (it does appear in two citations, but not in the sense Egnor refers to). So Egnor is wrong twice: the "accepted definition" of the word is neither simple nor straightforward, and the meaning Egnor claims is not an "accepted" one.
2. "Only man thinks abstractly; that is the ability to reason. No animal, no matter how clever, can think abstractly or reason."
Egnor's made this claim before, and it was refuted before. He just repeats it here, with no evidence, without addressing previous objections.
Of course, if you understand the theory of evolution, you realize his claim is likely to be utter nonsense. Abstract thinking is not a black-white thing; it's a range of capabilities that, even among people, we see a huge variation in. Any capability with huge variation is subject to selection, and so it can evolve. Since people are descended from earlier ape-like creatures, it is quite believable that non-human animals would also display the ability for abstract thought, in varying degrees. And they do! Ethologists, who actually study this kind of thing, disagree with Egnor. (Also see baboons and crows, to name just a couple more examples.)
3. "Reason is an immaterial power of the mind—it is abstracted from particular things, and cannot logically be produced by a material thing."
This is vintage Egnor -- a flat assertion, made with no evidence, and contradicting what we know about (for example) machine learning. Machines can abstract from specific cases to more general concepts; that is exactly what is done routinely in machine learning. (To cite just one example, see here.)
Egnor offers no rationale for why reason has to be "immaterial", and when he says something is "logical", you can be pretty sure there's no actual logic involved.
4. "This immaterial power of the soul is precisely what makes man qualitatively different from every other living thing. And I am not “forced to lean on supernaturalism” by pointing this out. I’m merely making an observation that’s obvious to all. Man, and man alone, has the power to reason."
Souls don't exist; there's no evidence for them. There's no evidence for "immaterial powers". Egnor's claim is disputed by many, and it's a plain lie to say it's "obvious to all".
5. "We routinely ask questions that entail reasoning. Animals never do."
How does Egnor know animals never do this? He never says.
As we know from the example of Ben Carson, it is perfectly possible for a neurosurgeon to be good at their job, but incompetent when it comes to anything else. Egnor is yet another data point.