During the Cuban Revolution, the Eisenhower administration called off all support for Batista's regime. This resulted in the pro-US regime falling, and giving rise to Castro's pro-Soviet regime.
Why stop supporting Batista?
I've heard it was over human rights. However, during his Presidency, Eisenhower:
Opened relations with dictator Francisco Franco in Spain
Overthrew the democratic government of Iran to establish the Shah's dictatorship
Supported Mobutu Sese Seko's rise to power in Zaire
Overthrew the democratic government of Guatemala to establish the dictatorship of Carlos Castillo Armas on behalf of the United Fruit Company
Human rights was not a large priority for Eisenhower in foreign policy. So what was his real reason for abandoning Batista?
The US Ambassador to Cuba even said, "Batista had always leaned toward the United States. I don't think we ever had a better friend."
The simplest answer for this is that support for Batista was becoming untenable. Yes, Batista was a great friend to the US, but:
He was running a dictatorial regime in the Cold War. The US was criticizing the hell out of the USSR for suppressing democratic movements in Soviet satellite states, but all the USSR had to do was point to support for Latin American dictators for the US to lose the moral high-ground. As such Washington wanted to slowly move away from dictators towards friendly, superficially democratic puppet regimes. For similar reasons they began distancing themselves from Trujillo in the Dominican Republic around the same time, although Trujillo just pushed on and only left power through being assassinated.
For all Batista's will to rule, he was unable to control the situation in Cuba. Guerrillas were slowly taking over the country, the military was divided and the instability was worrying, especially since Washington was hearing rumors that known Communists, like Ernesto "Che" Guevara and Raul Castro were among the leaders of the movement (Fidel was something of a mystery at this point, so many debated if he was secretly a Communist despite declarations of liberal democratic leanings). Washington knew that Batista was a focal point for the revolt and disorder, so they wanted Batista to step down so as to allow Cuba to cool off and a new pro-US regime to be installed. They were trying this until the last minute. Batista's refusal to cooperate is an important reason that when Batista finally fled Cuba he was prohibited from flying to Miami, causing him to fly first to the DR where he lived under Trujillo for a time.
I'd strongly suggest reading: That Infernal Little Cuban Republic by Lars Schoultz.