During the 1960's, the relations between USA and Cuba took a very bad direction. The two countries became enemies.
The reason for such a sudden turn in the relations was the Fidel Castro took over Cuba, implemented communist ideology, and also became an ally with the Soviet Union. The United States did not liked this at all as they had a communist neighbor right next door, and also a neighbor that enabled their arch enemy to set its weapons there.
The response of the USA on this was implementation of full scale embargo on Cuba. They tried to restrict the movement of Cuba's military in the surrounding waters. They even went so far that during the 1960's eight attempts were made to assassinate Fidel Castro.
Cuba responded adequately by threatening the USA that with the help of the Soviet Union they will shoot missiles on its territory and destroy it. In response to the attempts of assassination, Castro publicly said that if the USA continue with the attempts he will send hit-man to assassinate their president.