Languages do weird and wonderful things. Last year I had fun with "7 sentences that sound crazy but are still grammatical." This year I'd like to go over a few good reasons why people say, "I could care less." The list does not include "because they're stupid and have no idea how logic works." It turns out, there are a number of things about English that conspire to make "I could care less" a less irrational phrase than it might seem.
A number of language writers have suggested that "could care less" has a sarcastic reading, conveying something like "Ha! As if there were something in the world I could care less about." There are some American Yiddish-inflected phrases that work this way, like "I should be so lucky!" (meaning "there's no way I'm ever gonna be that lucky") or "I should care!" (why should I care?). Even if "could care less" didn't originate from a sarcastic intent, it matches up well enough with these other forms in the language to help give it staying power.
2. Positive/negative phrase pairs
Why use "could care less" if we also have "couldn't care less"? There are other pairs of phrases in English about which you could ask the same question. Why say "that will teach you to leave your car unlocked" when you really mean "that will teach you not to leave your car unlocked." Some other phrases that can mean the same thing with or without the negation:
You know squat about that. You don't know squat about that.
I wonder whether we can make that work. I wonder whether we can't make that work.
You shouldn't go, I think. You shouldn't go, I don't think.
I can hardly wait. I can't hardly wait.
Again, there's an existing framework that helps "could care less" blend right in.
3. Implied comparison
Evidence for the use of "could care less" goes back to 1955, with "couldn't care less" appearing only about 10 years before that. But long before that the phrase "No one could care less than I" was in use. Think about how you might respond to such a phrase in a certain type of conversation. "I've never been so insulted in my life! How dare they imply such a thing! No one could care less for the trappings of fame than I!"
"I could, darling. I could care less."
The rest of the comparison, "than you," is left understood. Perhaps "I could care less" also carries a shadow of the original phrase and a hidden comparison. "I could care less … than anyone."
4. Idioms don't care about logic
People might not have any thought of sarcasm, positive/negative phrase pairs, or implied comparison when they use "I could care less," but when they use it, it's as a set idiom, something they've heard before and learned as a unit. We have plenty of idioms that serve us perfectly well, despite the gaps in logic that appear if you look at them too closely. Consider "head over heels" (shouldn't it be heels over head?) or "have your cake and eat it too?" (shouldn't it be eat your cake and have it too?) or "the exception proves the rule" (shouldn't it be the exception invalidates the rule?). There are reasons these idioms developed the way they did, but we don't have to know anything about those reasons, or the original meanings, to use them perfectly sensibly. Same goes for "I could care less," which people only ever use to mean "I couldn't care less," never the opposite. It doesn't cause legitimate confusion, though it does cause quite a bit of consternation. In any case, it's here to stay.
For more on "could care less" see the collection of links on this topic at LanguageLog, columns by Jan Freeman at Boston Globe, John McIntyre at the Baltimore Sun, and Ben Zimmer at Visual Thesaurus, and the snappy overview by Bill Walsh in Yes, I Could Care Less: How to Be a Language Snob Without Being a Jerk.