I care about the Earth as far as it affects humanity. If white rhinos go extinct, that's sad, and the loss of biodiversity is harmful, but it's a fairly small thing. If, say, wheat were to go extinct, that would be a huge disaster.

The fact that our recent prosperity has come at the expense of the Earth is only bad in so far as that harm to the Earth is harmful to humans too. The two are linked, but not identical. The only way to eliminate human-induced harm to the Earth would be to eliminate humans, so the goal needs to be mitigation of harm and where possible moving harm to the Earth into areas that affect humans less.