Yeah this is why the Cuban Missile Crisis was a total farce. Lol to avoid catastrophe you just don’t push the button. Simple! The missiles don’t launch themselves, therefore no risk.
UPDATE: Thought of a good clarifying analogy. In one of the sequels to “Enders Game” the brother and sister of Ender adopted anonymous online personas and began writing. They were so skilled at politics and propaganda that they disrupted the entire world and the brother soon became world leader.
Or WW1? Or Vietnam?
Nope. Just pretty much rational people making locally-rational decisions inside a system where series of rational decisions yielded catastrophic outcomes. It’s entirely possible and history is full of such examples.