Everybody knows (but not everybody agrees) that the alleged problem with they/them is the ambiguity over whether the usage is singular or plural. Everybody who advocates using they/them can give examples where it’s perfectly clear that the usage is singular. But there are certainly cases where it’s ambiguous – you see a sentence with “they” and you can’t tell if it refers to one person or a group. (Sorry, I don’t have in example in mind at the moment. But I’ve certainly seen some.) I reject “they/them” as the third-person singular pronouns for this reason.
Most verbs in English do not need to be inflected to match the number of their subject. Inconveniently, though, it is exactly the third person present-tense verbs that do need to be marked for number – just the ones that cause problems when we try to use “they” for the subject.
A common but flawed rebuttal that always comes up is the fact that the second-person gender-neutral pronoun “you” is used for both singular and plural. The problem is, that’s just as bad. How often, even on this board, do we see this awkward construct: “… you (generic you)” or “you-all” or similar. The correct answer for this would be to re-instate the singular “thou” or something similar.
Strangely, we already have a perfectly cromulent gender-neutral third-person singular pronoun: “it” (which, in fact, a lot of other languages don’t have). Yet that is relegated to be used only for inanimate objects, or sometimes for animals. If pronoun usage were a bit more fluid, we could just as well have repurposed “it” to be the word we are looking for here.
Also, it is strange that there is so much fuss over the gendered pronouns in English, while overlooking how much gender has been eliminated in English compared with other languages. In Spanish, French, and so many other languages, even Hebrew, EVERY noun is gendered, even inanimate objects, usually arbitrarily, and adjectives must be inflected to match their nouns. In Hebrew, verbs must also be inflected to match the gender of their subjects. In English, our third-person singular pronouns, and a few nouns, are but vestigial remnants of gender in the language.