In 1961 after a long period of mutual help between Cuba and the USSR, Fidel Castro declares officially that the island will be ruled under the doctrines of communism; it is at the time the only communist country in the West. This is seen as a threat to the US, since Cuba is only 90 miles away from Miami. Moreover, there is a scare that a possible completion of the Truman doctrine will take place in Latin America.
Furthermore in 1961, J F Kennedy, the president of the US at the time supported an invasion of anti-Castro Cuban exiles that were stopped at the Bay of Pigs (from where the name of the invasion originates). The Bay of Pigs invasion was a complete fiasco that made the Americans aware of the increasing power of the island under the Castro Government.
The USA had to adopt the Monroe Doctrine once again; this doctrine states that the US has the right to intervene in Latin America to protect the Independence of its states; and therefore made the Americans more concerned about the existing communism in Cuba and the possible spread of it in other countries in Latin America.
The foreign policy of the USSR in the 60 tended to favor the spread of communism around the World; an opinion that was accented by the intentions of Castro to promote rebel governments across the states of Latin America. These were for the US proves that the threat of communism was constantly increasing.
In 1962, the Soviets sent masses of highly destructive missiles in Cuba where they were stored. When the Americans got aware of the existence of these missiles (after some pictures taken by spies) their scare of Cuba increased by the simple fact that the island is geographically positioned near the US, and therefore could destroy