Clearly people DO care so that is simply lying to yourself. And why would someone NOT want to care? Would you tell people to have this attitude with their career? With their kids? With their family or friends?I think a better mindset to try to adopt is an "I don't care" mindset.
Then why would you with relationships and dating? Sounds like a good attitude if you want to make no positive impacts on your life and be drifting in the ocean on a raft with no sail or paddle.