Well, JFK started that shit by putting Thor and Jupiter IRBM's in Britain, Italy, and worst of all, Turkey to the tune of nearly 300 total all of which could hit the Soviet Union. Up until he did that, the Soviets didn't give a flying fuck about Castro or Cuba. They just returned the favor in the form of a similar threat. JFK's military advisors had cautioned that putting IRBM's in Europe would piss the Soviets off and wasn't worth doing because within a year they'd have ICBM's in service in large numbers making the shorter ranged missiles unnecessary.
Kennedy, instead, listened to his idiot political appointees like McNamara who didn't know his ass from his elbow.
Then, all-of-a-sudden, when the Soviets started giving some payback, Kennedy's people panicked and freaked out about the Soviets doing exactly the same shit they did to the Soviets. The result was the Cuban missile crisis. And, at several points, it came down to one person NOT pushing the button, so-to-speak, that kept everybody out of a nuclear war. That was really too close to it happening that we should ever let it happen again.