In English, we use pronouns to take the place of a noun.

Amanda says that she doesn't want to go.

"She" is the pronoun that stands in for "Amanda." The noun that a pronoun refers to is called an "antecedent." So, "Amanda" is the antecedent for "she"

"Amanda says that they doesn't want to go" would make no sense. Since Amanda is singular and feminine, we have to use the singular, feminine pronoun "she." The pronoun "they" doesn't match. However, people do make this mistake in one case. Look at the following sentence:

A student left their backpack in the room.

How many students are there?? ONE! That means we must choose a singular pronoun. However, the pronoun here, "their" is PLURAL. Unless that student reproduced somewhere during the word "left," a singular cannot become plural. So, what are the singular pronouns? His or her!

See the problem? Because you don't know the gender of the student, you tend to just make it the gender-neutral "their"; however, this is wrong!!!! You have three solutions for this problem.

1. Make everything plural

Students left their backpacks in the room.
Oh, wait, that means something different, so we can't do it here.

2. Assume the male gender.

In Spanish, if you have a group of boys you might call them chicos (masculine). If you have a group of girls, you might call them chicas (feminine). If you have a group without knowing the gender, you call them chicos (masculine). So the masculine gender is used to indicate the people are male OR that the gender is unknown. English shares this rule with Spanish, so you can correctly say,

A student left his backpack in the room.
You are not letting the girls off the hook, you are simply implying that the gender is unknown.

3. Use both masculine and feminine singular pronouns

Since you don't know the gender, you can hedge your bets by including both genders.

A student left his or her backpack in the room.
Here you simply acknowledge that you don't know the gender.

 

Special Note:

I don't care which solution you prefer as long as you don't have multiplying pronouns in your sentences with singulars becoming plurals within the same sentence. However, some professors adamantly care. Some professors feel that solution two is sexist and that assuming a masculine when the gender is unknown implies a linguist prejudice toward men. These professors insist on solution one or three. Some professors feel that solution three is awkward and makes writing more difficult to read. They insist that solutions one and two are the only acceptable constructions under traditional English rules. In other words, you have to figure out what your professors want. When the professors hand out the syllabi (description of assignments), check them closely for pronouns. If all else fails, just privately ask your professors which solutions they prefer BEFORE handing in your first paper.

Someone needs to leave their dirty shoes outside because they left bootprints all over the floor.

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If a person wants to succeed in corporate life, you have to know the rules of the game.

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If anybody wants to succeed in corporate life, they have to know the rules of the game.

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Pen and Page's quick quiz
The Learning Center: Pronoun/Antecedent