Grammatically speaking, using the expression “I could care less” is to sarcastically push someone or something away. It is also a way of saying, “I could, but I don’t care” (as others above have pointed out).
Saying “I couldn’t care less” is a way of saying “It is difficult for me to care less about this or that.”
I think people use the expression “I could care less” as a means to separate themselves from a source of anxiety, frustration, pain, etc. It’s like waving the white flag and surrendering. Others might use the phrase to politely say, “fuck off!” or whatever explicative way of telling someone to back off.
I’ve used the phrase in the past when I tried to individuate myself from my family. I cared too much about their approval. However, saying or thinking “I could care less” eventually conflicted with my heart. It wasn’t that I didn’t care for them or about them. It was that I was overwhelmed and needed boundaries. So, I started using a different phrase: “I care not to care.”
Saying “I care not to care,” felt like I was really saying: “I do care. I’m a caring person. I care for ______. But, and this is a big but, I choose not to care or hold onto the things that keep me from becoming me.”