After Fidel Castro came to power in Cuba, he did two things that upset the United States immediately, he implemented the communist doctrine in the country, and he allied with the Soviet Union.
The implementation of communism in Cuba meant that everything that was private went into the possession of the government, including lot of companies that were owned by US citizens. That move was seen as robbery by the United States, as their citizens literary got their possessions confiscated without being paid anything.
The alliance with the Soviet Union upset and scared the United States. That move meant that their arch enemy will have influence over the island, and also probably make a military base just right of the coast of the United States, so that put them in a very bad tactical and strategic position.
