I think it gets presented incorrectly. The Earth will recover from whatever we do to it, but humanity won't. People are quite selfish by and large, the focus needs to shift to what we lose if we don't recycle or change our habits.
Your average punter doesn't care about an animal in another part of the world, but they'll soon notice when we run low on resources and all the prices shoot up.
So we absolutely should care, I just think if we want to see a difference in behaviour, we need to change the focus.