The Cold War had a greater chance of killing most of humanity than it appears due to survivor bias: dead people can't ponder their non-existence.
We collectively like to pat ourselves on the back for surviving the cold war, but it's not because we are smart or rational, but because of "survival bias". Those who survive but can't directly witness the "losers" can't make a fair assessment of the odds.
I'll give two examples to help illustrate:
1962: The partially-malfunctioning Soviet submarine "B-59" thought they were under attack due to misinterpretation of warning shots. The political Captain ordered a nuclear counter-strike, but out of a judgment call, the operations Captain, Vasily Arkhipov wanted to get more information before nuking, eventually figuring out that there wasn't a war raging.
1983: A Soviet station with a new type of radar detected what looked like five US missiles headed for Soviet territory. Lieutenant Colonel Stanislav Petrov was given the task of quickly deciding if the signals were real or just radar artifacts, as the Soviets started preparing for a nuclear counter attack. Out of purely a gut feeling, Petrov (correctly) concluded the 5 spots were merely a radar artifact. Petrov was given no time for a more thorough analysis before answering.
Had different people been at these two positions, there could have easily been a different outcome. And these incidences are just two of at least a dozen other cold war close calls. Assuming these were 50/50 calls, we'd have roughly a 50% chance of surviving one, 25% of two, 12.5% of three, 6.25% of four, etc. We shouldn't be here!
Thus, we are likely viewing the cold war with survival bias. If things went the other way, we wouldn't exist to discuss our failures. While such a war may not have killed every human, it would have likely killed every ancestor of ours alive at the time, and thus we ourselves wouldn't be around to ponder why the cold war failed humanity.