During the cold war Era (1945-1990), the United states and the Soviet Union were reluctant to become involved in direct military conflict mainly because

1. the peacekeeping role of the united nations
2. pressure from nonaligned nations
3. the potential for global nuclear destruction
4. increased tensions in the middle east

i was thinking about # 1 but im not sure if im right...?

I don't agree with your answer. The UN wasn't very important during the Cold War. But we were all scared to death of the possibilities of global nuclear destruction.