It was the fact that world super powers at the time (U.S) and (U.S.S.R) where building up an armory of nukes but they both knew if they where to use these weapons it would utterly destroy the world.
Here's a memory aid: (U.S): hey Russia lets not kill each other with nukes in this war lets just keep it "COOL" and spy on each other instead
The War did not occur directly on U.S. soil and the Americans played a relatively small role in the war, serving more as support for other nation's battles.
Those 2 countries are France and England