How was nuclear war avoided

During the cold war there were some very close calls but one of the closest was the Cuban Missile Crisis. The leaders on both sides didn't want to go to war but they were being pushed into it by the war mongering generals. Now the way I believe they avoided this was with empathy for each other. President Kenedy was constantly looking at it from the other sides perspective and trying to keep from blowing each other up. They also used back road politics so that both sides get what they want and both sides look like heroes for it. For example the Russians would remove their missiles and in return the americans would remove theirs. But there was on condition the Russians couldn't say it was a trade off and the americans would only remove their missiles six months later. The empathy and back road politics kept the world from going to nuclear war.