Why should "theirs" not have an apostrophe? [duplicate]
Solution 1:
It has nothing to do with possesive nouns and pronouns, and the use of the apostrophe here is consistent. An apostrophe appears wherever one or more letters have been removed.
Classically, we'd have written "Johnes things", instead of "John's things". So the apostrophe marks the absence of the letter E. This is why it does not appear in words like "hers" or "theirs".
Solution 2:
According to an earlier answer to another question, David Crystal's book The Fight for English: How language pundits ate, shot, and left says that lack of apostrophes in possessive pronouns was due to forgetfulness on the part of 19th century printers and grammarians:
Its is just as possessive as cat’s, but it doesn’t have an apostrophe. Why not? Because the printers and grammarians never thought the matter through. They applied their rule to nouns and forgot about pronouns, thus creating an exception (along with the food is hers, ours, yours, theirs) without realizing it. And even if they had noticed, they wouldn’t have done anything about it, for it’s was already taken, as it were, as the abbreviation of it is.
I don't know if that explanation is correct. It may merely be a long-winded way of saying no one knows.