Question

why was a buildup of weapons big enough for mutually assured destruction seen as a way to preserve peace?

Answer 1

The build up of nuclear weapons for MAD was seen as a way to preserve peace because people were afraid of the outcomes. Fear --> the knowledge that both sides would be destroyed in a war would prevent either sides from starting hostilities. Fear prevents war and therefore creates peace <---- if that makes sense.... :D [I just learnt about all this foreign policy stuff now i'm learning about the Cuban Missile Crisis :P]

Answer 2

Stalemate or a mutually assured Armageddon for any nuclear strike.
A "Mexican standoff" that is really a prolonged siege by both antagonists
that status quo is the only option.Since any nuclear strike will therefore trigger
an entire world destruction the entire world would group together and their combined
might would sway appease or compromise or usurp a ruthless antagonist