His or Her vs. Their
In the modern day and age, writers are looking for ways to write generic sentences without using gender-based pronouns. One of the ways is to use 'their'.
Why Do We Want to Use 'Their' instead of 'His or Her'?
In the past, it was common and normal to use the masculine pronouns (he, his, etc.) to refer to both males and females (people in general). But nowadays, this use of masculine or feminine pronouns for referring to people, in general, is considered unacceptable.
Nowadays, it is increasingly common to use the singular 'they' or its possessive form 'their' as a generic pronoun when referring to someone indefinite or unknown. This usage helps to avoid the gender-specific pronouns 'he' or 'she' when the gender of the person is not specified or when gender inclusivity is desired.
Everyone must do
In the past, the 'generic he' was supposed to refer to males and females generally.
Everyone must do
This was another alternative to avoid the use of 'generic he'. But, it is still considered sexist language and therefore still not acceptable.
Everyone must do
Do not confuse plural 'their' with singular 'their'. 'Everyone' is singular, but it is still acceptable and grammatically correct to use 'their' in this sentence.