Many people see a problem in the following sentence.
A person should take care of his pets.
The pronoun "his" is masculine -- it refers only to men. But women also have pets, and the noun "person" includes both men and women. English, however, does not have a singular, third-person pronoun that includes both men and women. To solve this problem, writers choose from several options.
1. If possible, make the antecedent plural:
People should take care of their pets.
Most people agree that this is a good solution, but it does not always work because antecedents cannot always be made plural -- "No one has been given her present yet."2. If possible, drop the pronoun:
"No one has been given a present yet."
3. Use the plural form of the pronoun --
A person should take care of their pets.
Although many people use this option, others don't like it because the plural "their" does not agree in number with the singular "person."4. Include both the masculine and feminine pronouns:
a.) A person should take care of his or her
There are two objections to these two options. First, many people find them both long and awkward. Second, they raise the question of which gender is mentioned first. (Perhaps men could always put "her" first, and women could put "his" first, but there is no agreement about this.)
Note that in some cases the masculine or feminine may be totally appropriate. A conductor talking to a male choir can appropriately say, "Will everyone please take his seat."