The theory is that saying "I couldn't care less" is like a double negative. So one should say, "I could care less." See?
However, scholars have scads of sites dedicated to this unfathomable saying...
The Oxford dictionary already recognizes “could care less” as an American colloquialism. Many people, however, regard it as incorrect since it makes no logical sense (if you “could care less” it means that you care at least a bit).

Frankly, I could give a damn...

I received a B+ in my first graduate level linguistics class. This despite having written a large, comprehensive, and (if I do say so myself) quite eloquent paper on the structure, history, and current usage of the negative particle ne and its forclusif partners (pas, rien, aucune, like that). Copies available on request.

French is an endlessly fascinating language : its construction of the verbal negative being one of those interesting points. It’s one of the few languages that requires two words to make a simple negative. Here, for example, are the ways to say “I do not eat” in a few romance languages (from Wikipedia):

French: Je ne mange pas.

Catalan: No menjo

Spanish: No como.

Portuguese: Não como.

Italian: Non mangio.

Romanian: Nu mănânc.

See how most everyone uses a single negative particle? Even in English, we only use one, except for when we use two, the so-called double negative. It’s often used to turn two negative words into a positive statement (”I don’t disagree”).

As a mathematician, though, my mind went to the fact that no language has the opposite construction : the double positive, where two positive words are used to construct negative. And I stated that fact when I presented my paper.

To which my professor flippantly replied “Yeah, right.”

Which I suppose explains the B+.