You are a big country now but you still tend to feel small and fragile. If the United States gets a cold you get pneumonia.
~ Herman Kahn
World War I broke out largely because of an arms race, and World War II because of the lack of an arms race.
From a scientific perspective there is some indication that a nuclear war could deplete the earth's ozone layer or, less likely, could bring on a new Ice Age - but there is no suggestion that either the created order or mankind would be destroyed in the process.
The widespread diffusion of nuclear weapons would make many nations able, and in some cases also create the pressure, to aggravate an on-going crisis, or even touch off a war between two other powers for purposes of their own.