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 prescriptivist grammarians decided they didn't like it, each for their own reasons.
BTW, do you really think that last sentence would be improved by saying "each for his or her own reasons"?
The modern resurgence of singular "they" is just returning English to what was common and correct usage before the prescriptivists hijacked the language.
