Actually, a nuclear holocaust would most likely not lead to all humans losing their lives. Many, if not most, would survive. Even some in the cities and their immediately surrounding areas would survive. Unless you tell everyone to go outside in the middle of their nearest city right before the bomb drops, you're going to be stuck with humans even after the dust settles.
And my point was that neither climate change nor nuclear holocaust would be sufficient to cause a mass extinction on the scale of, say, that which eliminated the dinosaurs. In either case there will be plenty of humans remaining.
Seems like a pretty unfounded assumption. Why do you think all of our knowledge and sources of societal stabilization are embedded in the communities most vulnerable to natural disaster?