I don't agree with this. I think the two are completely orthogonal. Your argument hinges on the assumption that saving the planet is strictly for the benefit of the humans living on the planet, and that seems wildly arrogant.
"If a tree falls in a forest"
This is not directed at you personally, but the view that humans are all that matters is a kind of species narcissism. In fact, we derive all sorts of benefits from other species, such that if all of them were to disappear, so would we.
We gain a ton of benefits from other animals, obviously. But if we don't exist, then those animals no longer matter. We wouldn't benefit from them anymore. Anyway, this is getting a bit in the weeds.