[JUAN GARCIA, repulsive dago queer]

Although i agree in essence with what you're saying, and the guy who started this thread is all wrong, you picked the worst possible example.

"Which is correct? a.) Everyone must use their toothbrush in private; or b.) Everyone must use his toothbrush in private."

What you say is true in a theoretical sense; in common speech, less so. Language usage is not determined by any absolute standard, forever immutable; it's changing literally as we speak.

The difficulty with your example is the lack of an indefinite third person pronoun in English, so that one is forced to choose (in your example) either "his" or "her" or the awkward "his/her," which doesn't add any clarity to the sentence. Many people, therefore, use "their" instead. Given the circumstances, and the number of people who employ this usage, it cannot be said to be wrong (although a good writer will rewrite the sentence to avoid the situation), and the more people who use it the more right it becomes.