Indefinite pronouns enable us to refer to any one, any two, several, or all in a group or class of persons or things or ideas. Examples include: all, another, anyone, each, someone, everybody, none, others. Some of the pronouns have possessive forms (someone's, everybody's). Some don't: There's no possessive of none, for example. Unlike the personal pronouns, the indefinite pronouns form their possessives by adding “apostrophe ‑s.” Only one has a plural form (others). In formal settings, all indefinite pronouns ending in ‑one or ‑body are singular. You should therefore use singular verbs. And, in formal settings, when referring back to them, you should use singular pronouns.
For a thorough discussion, study the section on Pronouns in Parts of Speech on Grammar.com. Click here for the beginning of that discussion.
Everybody is entitled to their own opinion. (One day, even highly literate Americans will regard this usage as correct.)