I always assumed that pretty much everyone knew that the phrase “I could care less” doesn’t make literal sense. I assumed it was simply an unfortunate shortened form of “I couldn’t care less”. I think it’s popular because it has better cadence. It might be helped along by the likely element of sarcasm in it.
According to The Internet, and the occasional journalist, though, I’m wrong. Everyone who says “I could care less” is a dunce incapable of calculating the literal meanings of words. They’ll present us with fancy Venn diagrams and bar charts to try to get it through our thick skulls that “less” is less than “more”.
Language is weird, or course. Consider that “I care little” and “I care a little” superficially look like they should mean the same thing, though they’re actually almost opposites. But I don’t think that’s what’s going on with “I could care less”. I don’t think it’s a roundabout way of saying “I care little” — though you could try to use that as a defense.
It’s hardly the only phrase that means the opposite of what it could mean if taken literally. Others include “head over heels”, “no love lost”, and double negatives like “ain’t got no”.
A similar phenomenon is unfortunate abbreviations, where the critical part of the original phrase gets left out, so what remains is just wrong in some way. Like abbreviating “Wikipedia” as “Wiki”, or “IP address” as “IP”, or “cryptocurrency” as “crypto”. These things do bug me, and I reserve the right to occasionally call people out on them. But I’ll try not to get too bent out of shape about it. It’s usually a losing battle. I don’t want to be the guy on record saying “It’s not a car; it’s a horseless carriage! The whole point of the term is to distinguish it from a horseFUL carriage, so you can’t just leave out the horse part!”