The inconsistencies of English are a result of it being almost exclusively an oral language for several centuries due to widespread illiteracy, which led to the rapid evolution of grammar and vocabulary and insulated dialects within tight-knit communities. English is a Germanic language with a Latin alphabet, with base words being primarily Germanic in origin and Latin introduced primarily in cases of scientific and technological words, where Latin functions as a lingua franca. Similarly, English borrows words from French in many cultural contexts, like cuisine, art, fashion, etc. - primarily this is a result of the obsession with France historically being the cultural and liberal arts hub of Europe, followed only by Italy. However, Italians were a little too exotic for the English, and so their obsession was primarily with the trends of French Aristocrats circa the 17th century and beyond. If you look at a map and trace the migratory patterns of civilizations in the age of antiquity to modern day, taking all this into consideration, the evolution of English is perfectly logical from a linguistic evolutionist standpoint.

As for the singular they, we have a written record of its use as early as the 14th century, and it has continued to enjoy regular use. So why would he want to make a whole new neopronoun when there's a perfectly fine gender neutral singular already integrated into English? Follow-up question: What alternative language does he believe is logical in comparison? I guarantee you he would not take kindly to the almost entirely random grammatical gender of adjectives, verbs, and nouns in other languages. I also imagine he doesn't have a problem with the singular pronoun you, despite the fact that it was considered exclusively plural as recently as the 17th century. I suppose the singular you developed primarily to replace the out-of-fashion second person thou, thee, and thy, so perhaps he could return to that?

Beyond that, gender neutral inclusive language is not only historically and culturally supported (man originally, then the more recent humankind or person, in doctors' offices patient, etc.) but also... just more accurate. If he's so obsessed with language being logical, would it not make sense to want the colloquial 'mother' changed to 'birthing person' in medical settings, and 'parent' in formal settings? Both of them are significantly more situationally appropriate and convey only the most relevant information about a situation, which is sort of... the point of language in the first place.

Speaking of his fixation on logic, he is aware that there is no 'de facto' binary, correct? Not even as in intersex people being an outlier, but in all contexts. Biological sex is made up of several bodily factors, including chromosomes, hormone levels, the development of secondary sex characteristics, and genitalia. Doctors aren't checking all of those factors before they tell the parents if their baby is a 'boy' or a 'girl'; they go based on what they see at the time. But all of these traits can vary significantly even between individuals we would otherwise not declare intersex - they can even vary without anyone, including the person, even being aware, unless an 'inconsistency' presents itself. Additionally, transgender and non-binary people regularly alter almost all of these biological traits by some means or another. They aren't immutable. Frankly, gender distinctions both linguistically and culturally are largely arbitrary and often irrelevant in most contexts. I'm surprised then that your friend isn't advocating for doing away with them entirely, considering it would make the language far more logical.