Earlier quoted context omitted.
Because writing in English requires either gender specific singular pronouns or the awkward sounding use of a gender neutral _plural_ pronoun referring to a singular person.
There is no rule in English that says a pronoun cannot be both singular and plural. Here's a simple example: "Which of you thinks you are the smartest?" I used "you" as both singular and plural in that sentence, and no one would blink an eye at it. "They" is used the same way as "you", as either a singular or plural pronoun depending on the context. This was the case in English for centuries, until some prescriptivis…
I would think that this is a mistake and you'd need to say:
"Which of you thinks he or she is the smartest?"
I'm not a native speaker though.