I don't really think of catastrophic climate change as causing human extinction. Not at all. We will cause innumerable other species to become extinct but not ourselves. What we will do is mess up God's bountiful good Earth and pay a heavy price for doing so, but it wouldn't be the end of us. Just the end of the good times. The end of the age of plenty and the beginning of the age of scarcity and a whole lot of misery but we will still live through it all.
The good news is that even if we really f'up real bad and turn the Earth into a desert wasteland, we are clever enough to recreate the Earth into at least an adequate habitat. I mean a lawn of crab grass isn't the same as an old growth forest but it is better than bare concrete. That's how I think of it. We turn the Earth into a catastrophe - a wasteland for most species, they'll go extinct and we eventually get sick of living surrounded by bare dirt and city streets. We plant grass and some shade trees and call that nature. Just us and the roaches, the mice, the rats, thecats and dogs, (and f'n pigeons) and our edible domestic animals. No more Lions, Tigers and Bears Oh my. No way no more. Just us and our ...farm like habitat.
The bounty will be gone but we will still be here... and will need to make the best of what we have left.