This is a common reply I see. I'd argue our impact on the very systems of life is now large enough that there's far from a non-zero risk that we do in fact take the systems that sustain life on the planet with us.
So the planet as rock in space is indeed likely to outlive us but the planet as a host of life is less clear cut.
There has never been a species before that has pulled so heavily on the web of life and that's why its even more important to fight with every last breath to try and fight to protect the only source of life we are aware of in the universe.