Consider this sentence:
“Each person must write their own autobiography.”
Do you see the problem here? “Each” refers to one person, but “their” refers to more than one person.
Some writers intentionally make this common mistake to avoid the correct his (which sounds sexist) or the cumbersome his and her. Most make this mistake unconsciously. Consider this incorrect sentence:
“Any professional writer will edit their own documents.”
This has the same problem as the first example. If the subject is singular, our preference is to use his and her or its similar expressions: he and she, his and hers, him and her, etc.
While these phrases are correct, they can make sentences sound redundant. Consider this sentence.
“Each team member took his or her uniform to his or her mother to clean for him or her.”
The better option is to find the antecedent for the pronoun and make it plural. In this way, we revise the previous example as,
“The team members took their uniforms to their mothers to clean for them.”
If the antecedent of the pronoun needs to remain singular, use the correct version of his or her.