Why did US want Fidel Castro out of power?

Because of the 1962 Cuban Missile Crisis. Castro wanted to start nuclear war because he believed that the US would nuke him first. So Fidel wrote a letter to Nikita Sergeyevich Krushchev that basically said that if there was going to be a nuclear war, Russia should launch their missiles first. Luckily Krushchev didnt agree with him (that was the Cuban Missile crisis), and everyone thought he was insane for wanting to start nuclear war.