grammatical number - Why use the plural form for a single person?

Being a non-English native, I'm surprised when I read people who use a plural form when they're clearly talking about a single person.

Here are two excerpts from a software I used to work on, written by a former Irish co-worker:

... a supervisor must assign it to themselves and deal with it.

and:

This supervisor has no restaurants assigned to them.

I would have written the following sentences instead:

... a supervisor must assign it to himself and deal with it.

and:

This supervisor has no restaurants assigned to him.

Is the plural form correct English, and if so, is the plural preferred over the singular form?

Answer

Singular they is widely used as a gender-neutral pronoun to refer to a single person.

A reason for its use is that English has no dedicated singular personal pronoun of indeterminate gender.^[5] In some cases, its use can be explained by notional agreement because words like "everyone", though singular in form, are plural in meaning.^[6] Its use in formal English has increased in recent times with the trend toward gender-inclusive language,^[4] but it has been used by respected writers for centuries.^[7]

Though singular "they" has a long history of usage and is common in everyday English, its use has been criticized since the late nineteenth century, and acceptance varies.