In this environment, caring becomes not just "not worth it" but can be actually detrimental, as it opens you up to a lot of pain. To pick a random banal example, if you care what you eat, you'll be disappointed when the local tasty restaurant is replace by a McDonald's, but if you don't, you won't.
I have to add that the author's exhortation at the end still strikes me as a bit tone-deaf. There are plenty of people who want to care, and even still do care, about things. We don't need to tell people to care. What we need to do is take a sledgehammer to everything and everyone that makes not-caring the easier choice.