Pronoun error

My problem with grammar today is pronouns. I never really thought about this to much but when I referred to "their" instead of his or her, I was marked wrong on my paper.

So here is the rule, in order for a pronoun to be correct the noun must match in number.
For example,

• Pronoun error: Everyone needs to bring their own canteen.

• Correction: Everyone needs to bring his or her own canteen.

Even though everyone seems plural it is actually singular. So if the noun is singular than the pronoun must be singular as well, therefore making it "his or her own canteen", not "their own canteen."
For more information go to http://college.cengage.com/devenglish/fawcett/evergreen/7e/students/grammar_errors.html