Who are the people that actually claimed "that a full-scale nuclear war is likely to cause human extinction?" I don't think I've ever heard anyone say that. It would cause societal collapse, perhaps even an extinction of civilization, but not a literal extinction of our species.
I'm sure I've heard the idea that nuclear arsenals can kill us all a hundred times over, or similar. Obviously my half-remembering isn't evidence, but if other people had heard this sort of thing, it would be evidence of a popular idea, however wrong. Even allowing for the larger arsenals at the height of the cold war.
Today arsenals are so much smaller than during the Cold War. Both the US and the USSR had almost 70K warheads; today they have 1600 each. Reading about SIOP plans makes you realize how hard the US planned to hit the USSR; I have no doubts the Soviets had similar plans. Today, 3200 warheads can ruin your day; but 140K warheads (discounting the relatively small number of Chinese/French/UK warheads) would ruin all but the Southern Hemisphere.
Ok, say 10% fails upon launch or fails to detonate. Now you're down to 63K per side. Say each side reserves 50% for targets of opportunity, they've each launched 31K warheads. Goodbye civilization.
The UN reports that there are currently 580 cities in the world with populations greater than 1M. Doesn't take many warheads or launchers to wipe those out.
In several decades of seeing stray discussions online about nuclear war, including here on HN, I've yet to see a discussion where human extinction wasn't a commonly assumed outcome.
It's almost always thrown out as a matter-of-fact inevitability, it's assumed. It appeals to the self-hating cult of 'humans deserve it.' I'd wager the people that float that theory more often than not tend to hate humanity and are lusting for its destruction, so that appeals to them, they want it to happen and are projecting irrationally outward.
