This is one of my biggest pet peeves.

When we say “I couldn’t care less” (or “I could care less”), we’re essentially trying to say “I don’t care.”

If we say “I could care less,” that logically means “I care, but I could care a little less.“ So this doesn’t mean “I don’t care.” Right?

On the other hand, if we say “I couldn’t care less,” that means “I care so little, I can’t possibly care any less than I do.” In other words, I don’t care. BINGO.

TL;DR: "I COULDN’T care less” is right.