Additionally, the practical reason that people often use this form of words is if you are referring to someone of an unknown gender, to use
he, him, his, etc. is nowadays considered
sexist. Using
them, they, or
their is a way to avoid making an assumption of gender as there is no gender explicit in these pronouns. Find out
more about gender-neutral language. Second, people prefer not to use
he or she,
him or her, etc. because they are
long-winded and can be distracting, especially if they have to be repeated several times in the same sentence or paragraph.
Despite objections, there is a trend to use ‘singular they’. In fact, it is historically long established. It goes back at least to the 16th century, and writers such as Shakespeare, Sidney, Byron, and Ruskin used it:
There's not a man I meet but doth salute me
As if I were their well-acquainted friend (Shakespeare’s
The Comedy of Errors)
Whether it is grammatically correct is is a matter of opinion. Two things are matters of fact, however: many people use it, and many others dislike it intensely. If you are writing something, it is therefore advisable to consider who might read it, and what their views might be.