grammaticality - Which is correct, "you and I" or "you and me"?

When the phrase is used as an object, why so many native speakers are saying "you and I" instead of "you and me"? I'm not a native speaker but I thought "you and me" is correct. Not sure if this falls into the same category, but "Just between you and me" sounds more natural than "Just between you and I".

Answer

This is an example of hypercorrection, which is when native speakers make an accidental error in their zeal to avoid a different error.

In this case, the error that's being avoided is the error of writing "you and me" in subject position, as in the following sentence:

You and me are going to the store.

This is formally incorrect, although it's very common in contemporary spoken English. Because they have been taught that this is incorrect, many people hypercorrect and change "you and me" to "you and I" in all positions. That is, they incorrectly learn the rule about when to use "you and I", and so produce sentences like the following:

You and I are going to the store. [Correct]

He'll come to the store with you and I. [Incorrect]