I'm in love with a proofreading woman
I'm gonna love her till the day I die
She's got a big dictionary and real good grammar
She never says "between you and I".
Not as bad as this song, but come on, what's wrong with saying "between you and I"? I don't write about grammar much because Motivated Grammar does it so unfairly well, but I think it's worth talking about this construction.
Merriam-Webster's Dictionary of English Usage says that between you and I "seems to have no place in modern edited prose" but that it can be normal in informal speech and prose representing informal speech. It's been used by Shakespeare, Congreve, Pepys, Byron, Fitzgerald, and Defoe, and we keep using it, despite the many attempts to make us stop. Most recently I encountered it in Hot Fuzz (in the scene in the flower shop).
Since it has been used as early as 1596 (in The Merchant of Venice), and English grammar only began to be taught in the 18th century, hypercorrection cannot be the sole cause. Merriam-Webster's Dictionary of English Usage identifies two uses for between you and I. One, which they call confidential, occurs mainly in spoken English and conversational prose.
...without speaking disrespectfully of the sweet town; (which between you and I; I wish was swallowed up by an Earthquake...) - Lord Byron, letter, April 23 1805
The other, called "transactional," is not confidential, and indicates a transaction between two people.
All debts are clear'd between you and I - Shakespeare, The Merchant of Venice, Act 3, scene 2, 1596
There was nothing between Mr. Robert and I - Daniel Defoe, Moll Flanders, 1722
Both the confidential and transactional forms are mainly spoken forms. Neither between you and I or between you and me occurs much in print at all, but when it does occur in print, between you and me is usually found.
It's different from other "preposition + X and I" constructions, for instance this one used by Prince Charles: "For my wife and I it really is the greatest possible joy to be in Pakistan." A prescriptivist might argue that for my wife and I is wrong because for I is wrong. But that doesn't work with between. Between requires two or more elements. You can't remove one of the pronouns from between you and I and still have it make any sense. For this reason I think between you and I is approaching something like an idiom.
This thesis looks at possible reasons for why two pronouns joined by and behave differently than single pronouns, and suggests that object-position "X and I" is a natural extension of subject-position "X and I", perhaps reinforced by, but not caused by, hypercorrection. Since subject-position "X and I" is more frequent than object-position "s/he and X", the former is more likely to be extended into object position. Furthermore, "X and I" is a prestige form (it's considered more polite), and so is more accepted in object position than "me and X" is accepted in subject position.