their
/ᴛʜâr/
adjective
- Used as a modifier before a noun. their accomplishments; their home town.
- (Usage Problem) His, her, or its.
Each of the horses has their own food formula, which is carefully worked out by a dietician.
Why is their in this sentence incorrect? Probably just missing something easy.
pronouns - Is it correct to use "their" when referring to a single person when the gender is known? - English Language & Usage Stack Exchange
CMV: Using the pronoun "they/them" is confusing and it should be changed
What do the pronouns 'they/them' mean?
Why do people use “she/they” or “He/they” as their pronouns?
What are the meanings of there, their, and they’re?
When should you use there, their, and they’re?
Example of there, their, and they’re
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"Correct" is opinion as English is a natural language, and is therefore off topic.
However, "usual" and "accepted" are measurable and therefore valid questions. My experience suggests that the use of the singular they is spreading at an accelerating rate down this list :
Gender unknown (the doctor I will see tomorrow)
Gender hidden (my partner if I choose to hide their gender)
Gender irrelevant (the doctor I saw yesterday)
Unspecified person of known gender (the woman in question)
Specified person of known gender (my girlfriend)
My experience is that as people are criticised more and more for politically incorrect use of he or she but almost never criticised for they except by pedants, people (especially children) are increasingly using they as it's easier than thinking which is correct.
"Correct" is a social judgment, not a linguistic one.
The OED has examples of singular their going back to 1382, but there are still people around who think there is something wrong with it.
If you care about being judged by people who think that, then don't use it. The rest of us will carry on using this useful English word with a long history.