couldn’t care less
If you could care less, you care somewhat. That is the opposite of your point.
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Wrong: I could care less.
Right: I couldn’t care less.
Could care less means there’s room below zero. You meant there isn’t.
The logic
The phrase claims your level of caring is at absolute zero—you could not care less than this, because there is no less.
Drop the n’t and you’ve said the opposite: you could care less, which means you currently care at least somewhat.
The defence, and why it’s thin
Some argue the shortened version is sarcastic—oh, I could care less—and sarcasm inverts it back. That’s plausible for the people who say it that way and generous to everyone else, who are plainly just dropping a syllable they didn’t notice.
One contraction fixes it, and then nobody has to have this conversation.
Now go put the n’t back.