Why didn't we blow ourselves up during the Cold War?

After completing that simulation today in class- it's hard to see why we didn't blow ourselves up. The USSR gave us an ultimatum that we didn't want to follow or abide by, so we went against their wishes but i didn't actually think they'd blow us up. I mean, I honestly wanted to blow them up too, but this is just a game: not the real thing. I definitely couldn't live with knowing that I killed MILLIONS of people with the push of a button. They had a partial victory and we had total defeat: okay, i can live with that. I realize my team didn't save the United States, but at least we didn't succumb to their level and resort to blowing things up in order to get their way. That's one of the reasons I think we didn't all blow the world up- it's because no one wanted to be the first to strike, no one wanted to be blamed for the war. If the USSR shot first, then we could counterattack and blame all the destruction on the evil communists. BUT if we struck first than all the blame would be on us. We would be blamed for all the destruction and deaths in the USSR and the US citizens (that would still be alive) would find it hard to blame the USSR for something that they didn't even start. It's just like in any fight, both sides want to win and blow stuff up, but no one also wants to strike first. It's partially about fear as well, fear of what exactly would happen if we pushed the button and nuked the world. I know they all saw what happened in Nagasaki and Hiroshima, but that's Asia- what exactly would our home country, the USA, look like if most of it was ruins, ruins, and more ruins covered in nuclear radiation? Therefore, I think that we didn't blow ourselves up during the Cold War because we were scared of what would happen and we didn't want to be blamed for the destruction of the world. I mean, who would want that kind of guilt? the guilt of killing millions! DAVID JONATHAN AND NATE! YOU KILLED MILLIONS/you destroyed the USA! OH WELL!