The rule: Pronouns should agree in number with their antecedents.
One of the limitations of the English language is its lack of gender-neutral singular pronouns that refer to people. Singular pronouns are either masculine (he/him/his/himself) or feminine (she/her/herself), or they refer to things, not people (it/its/itself).
Anyone who wants to go swimming should bring their bathing suit.
This type of sentence structure is extremely common in informal speech and writing, but according to the rules of standard American English, it contains an error in pronoun/antecedent agreement. The singular indefinite pronoun "anyone" does not agree in number with the plural personal pronoun "their." One way to avoid this agreement error is to replace "their" with "his or her."
Anyone who wants to go swimming should bring his or her bathing suit.
Errors in pronoun/antecedent agreement are often found in questions on standardized examinations, and answer choices may include "his or her" when the antecedent is singular. Sometimes "his or her" may not be an option; questions may include only "him" or only "her" as a choice. It is preferable to assign a gender to a pronoun (even if no reference to gender is made in the sentence) than to use a plural pronoun to refer to a singular antecedent.
One way to avoid using the somewhat awkward "his or her" or assigning a gender with the use of "his" or "her" is to rewrite the sentence using a plural antecedent.
People who want to go swimming should bring their bathing suits.
The plural pronoun "their" now agrees in number with the plural antecedent "people." Notice that the singular noun "bathing suit" was changed to its plural form to indicate that each person has his or her own bathing suit.
Some people who study language believe that the use of plural pronouns (they/them/their/themselves) to refer to singular antecedents has become so common that the rules should be changed to allow this usage. At this point, however, the rule stands: pronouns should agree in number with their antecedents. Answer standardized test questions accordingly, and remember this rule when you are writing to avoid offending readers who adhere to it.
