The Soviet Union and United States were so fearful because of M.A.D (Mutually Assured Destruction) which means if one launched a nuke, the other would launch a nuke, and so on with there Allies. One event that brought us to that point was President Richard Nixon's , Mad Man Theory which he purposely acted as irrational and volatile as possible so the Soviet Union would avoid provoking the United States. At one point the United States Millitary was ordered to had fully armed bombers with thermonuclear weapons fly patterns right on the edge of the Soviet border, which made the Soviets ready to push the button if it started to fly(even by accident) over there border from fear.