pronouns - Why do we say "of mine/of his" instead of "of me/of him"?

He's a friend of mine.
That's a car of his.

Why do we use the possessive when the meaning would be the same while not using it (e.g. a friend of me and a car of him)? I thought maybe it is short for That's a car of his [cars], but I have no way of making sure; it sounds a little odd that way to me.

Answer

They're examples of the double genitive/possessive, which is perfectly valid and has been around in English for centuries. The of already denotes "possession", but we do this again when we use mine/his instead of me/him.

The fact that we don't say John is a friend of me/him is really just idiomatic for those particular forms. But that "idiomatic principle" isn't universally observed - people often say, for example, He's a friend of John. Though they also say a friend of John's - both forms are valid there.

Here's an NGram showing how friend of her has gradually given way to friend of hers over the past couple of centuries, as the "reach" of the idiomatic mine/his has been extended.