I don't actually understand the downvotes you are getting, unless people think that this just isn't adding to the conversation, but in the interests of making lemonaide:

We often use neuter (gender-neutral) pronouns in English, just not this one. I've heard native English speakers say things like "If a mother wants to use the nursing room, they can just key in the code in their pamphlet". There are definitely restrictions on using 'gender-neutral they' but this kind of usage is totally normal.

Which is a great sentence, because semantically the pronoun referent is obligatorily female and singular. And yet, we use 'they' in this context. Which shows (among other things) that syntactic requirements can be relatively divorced from semantics. C'mon, that's pretty cool, right?