It’s always been a mystery to me why some people (especially Americans) say “I could care less”. If you “could care less”, you express indifference—you care somewhat, so you could care also less. You could perhaps care even more.
The point of the idiom is to express that you don’t care. In fact, you care so little that you couldn’t care less; you’ve already hit the bottom of how much care you give:
Some linguists suggest that “could care less” is so widespread that it should be considered an acceptable variant of “couldn’t care less”, but the fact is, many people consider “could care less” to be simply wrong and its use to be a sign of lack of education, so if you want to use the expression, it is better to stick to the variant with “not”, which is still more common and which most people find acceptable.