Your faith in rational human behavior is much stronger than mine. All it takes is one person making an irrational decision (driven by anger, false sense of security, accident or other) to essentially doom everyone. Death-row is filled with people who made similar decisions (do something even though the consequences of that were dire), all it takes is one person making a similar decision on a bigger scale.

MAD doesn't prevent anything, it at best postpones things and at worst forces both sides to escalate to the point where they feel they can completely destroy the other even given significant losses (i.e. building significantly more bombs than they need to destroy the planet).