Word peeve: Could you care any less?

Are you one of the people who says, "I couldn't care less"? Or are you one of those who says, "I could care less"? (We'll talk about inside vs. outside punctuation another day.) Which is correct?

Well, let's consider the derivation of the phrase, as an extreme version of "I don't care."  It goes like this:

I don't care about it.

I really don't care about it. Not at all. Zero. Zip. Zilch. Nada.

In fact, I care so little about it that you can't even measure how little I care about it.

There is no way in this world I could possibly care any less about it, than I do right now. It's a mathematical impossibility. You can't care less than zero.

In other words, I couldn't care less.

That works for me. So what's the derivation of the other one? I dunno. All I can think of is this:

I don't care about it.

But if you argue with me, and insist that I do care, even a smidgen, then I could probably force myself to care even less, just to prove to you that I don't care. But it's not worth the effort.

Nope. It sounds too contrived to me. I'm sure they're both listed in the dictionary, just because the "could" one has been in use for over 50 years.

But I'll insist that it's still wrong, and I will kick until my feet are bloody against this cursed evolution of the English language. I know that none of you care. In fact, you probably couldn't care any less.

My feet are all bloody, and nobody cares. *sob*