Everybody should mind his/her/their(?) own business.

Question

Why is it acceptable to use their with singular pronouns such as everybody? Example: Everybody should mind their own business. - Moses

Answer

Thank you for asking this question that both native speakers and English learners often struggle with. 

You are correct that the indefinite pronoun everybody is a singular pronoun, like the pronoun everyone, even though conceptually these pronouns represent groups of people. These singular pronouns take singular verbs, as shown in the sentences below:

• Everybody needs to bring money. ("needs" is singular)
• Everyone wants a new bicycle. ("wants" is singular)

Although it is grammatical to use singular pronouns and possessives to refer back to these pronouns later in a sentence, most people don't. The majority of speakers of American English, except in very formal contexts, will use plural pronouns and possessives, as shown in these examples:

• Everyone chooses what they want to have for dessert. 
• Everybody puts their own dishes in the dishwasher. 

More tradition-minded speakers may stick to singular pronouns and possessives, but these can end up sounding awkward, because English has no singular, gender-neutral pronouns and possessives for people. Therefore, one has to make a choice between the feminine and masculine forms, or use both:

• Everyone chooses what he or she wants to have for dessert. ("he or she" can sound wordy and awkward)
• Everybody left his dirty dishes in the sink. ("his" doesn't work well if it is being applied to both men and women)

I hope this helps.