Ok bro you made me pull up the wiki:

Why Khrushchev blinked:

Castro, on the other hand, was convinced that an invasion of Cuba was soon at hand, and on October 26, he sent a telegram to Khrushchev that appeared to call for a pre-emptive nuclear strike on the US in case of attack. In a 2010 interview, Castro expressed regret about his 1962 stance on first use: "After I've seen what I've seen, and knowing what I know now, it wasn't worth it at all."[102] Castro also ordered all anti-aircraft weapons in Cuba to fire on any US aircraft; On October 28, 1962, Khrushchev told his son Sergei that the shooting down of Anderson's U-2 was by the "Cuban military at the direction of Raul Castro".

At this point, Khrushchev knew things the US did not. First, that the shooting down of the U-2 by a Soviet missile violated direct orders from Moscow, and Cuban anti-aircraft fire against other US reconnaissance aircraft also violated direct orders from Khrushchev to Castro.[131] Second, the Soviets already had 162 nuclear warheads on Cuba that the US did not then believe were there.[132] Third, the Soviets and Cubans on the island would almost certainly have responded to an invasion by using those nuclear weapons, even though Castro believed that every human in Cuba would likely die as a result.

Basically Castro was a lunatic that didn't care if Cuba got glassed. Maybe he thought he would get 40 virgin gopniks in Communism. Castro affirmed his desire for nuclear war in an interview in 1992, and then expressed regret in 2010.

Khrushchev did not want nuclear war. Castro did. Khrushchev knew that he couldn't control Castro from Moscow, so rather than give Castro the opportunity to start WW3, Khrushchev rug pulled him and caved in. Khrushchev "lost" and suffered a loss of face, because that was preferable to death.

While there might be an occasional lunatic like Castro out there, the Soviet/Russian nuclear arsenal is safeguarded against such people. It is controlled by people who don't want to die anymore than NATO does, which is why this nuclear brinkmanship from Putin, if it works, will create a very dangerous situation, which is why we need to stand up to it and not allow him to think that it is working. Show no fear.