Let’s review a confusion in English grammar more common than it need be. Do I say keep this between you and me or keep this between you and I? The question before us is not why should I care; that’s a concern that would take us into the reaches of the philosophy of art. Let’s assume we do care, that we take the proprieties of craft to be important. What, then, is the difference between these two sentences?
What is at issue here is a department of grammar called case. It’s an odd word with an interesting derivation, but case refers to nothing more than how a noun or pronoun changes its spelling or position in a sentence to show its grammatical function. And that’s about as concisely as I can state it. English has three cases, and each case has associated with it a number of grammatical roles. Find the appropriate case for the function at hand, and you can decide and revise confidently. Compared with some other languages, English does not change the spelling of its words very much to show how a word is being used grammatically. When it does (a phenomenon called inflection), we can see it most easily in the personal pronouns.
The difference, then, between I, my, and me, is the difference between the three cases: nominative, possessive, and objective, respectively. To say that I is the nominative case of a personal pronoun in English means I is the form of the pronoun we use when we intend to name the subject of a clause. Likewise, me as the objective pronoun means we use that form of the word to identify the object of a verb or preposition. We say, for example, I went out to dinner with him last night, not me went out to dinner with he last night. The second version will strike most readers and speakers of English as wildly incorrect, and most would rely on their ear to, well, decide the case. But our ear is actually too sophisticated an instrument to conclude grammatical questions (being better suited to the subtleties of rhetoric), and we will often rely on it to our disappointment.
And we often come to disappointment because our ear simply records the grammar it hears. For example, we very commonly hear the construction between you and I, and if we were thoroughly democratic, thoroughly to the point of unreachably individualistic, then that, and any other arrangement of words I might prefer, would be acceptable, even to the point of unintelligibility. What would matter is that I did what I wanted. Short of that extreme, though, we want to be understood, presumably because we care about what we think. Being understood involves other people, and we need some bridge to span the differences between us. Thus the rules, so called, of the common, or standard, version of a language (or any other art), so that everyone is included. And that brings us right back to the phenomenon of case.
So why not between you and I? We know the answer already. Between is a preposition. Every preposition must have an object, and the object of a preposition is in the objective case. But I is the nominative case of the pronoun, not the objective, and so we must revise the phrase to between you and me, no matter what our ear may say about the change, at least grammatically. This device of case can be relied on to settle questions of comparison and the infamous who and whom confusion as well. Entities being compared are placed in the same case (so we say he is taller than I, not he is taller than me), and whom is simply the objective form of the relative pronoun who (so we say the person whom I hired, not who I hired).
But the ear will have its day and due. Using language well is never merely a matter of grammatical etiquette, or even precision. We must also take into account the circumstances and purpose of the moment, and scale our constructions accordingly. What matters most, though, is that we know the reason behind the choice we are making, and then the choice is ours to make.