Final answer:
Americans feared Fidel Castro's takeover of Cuba due to the threat of communism spreading just off the US coast, resulting in national security concerns. The Bay of Pigs Invasion and subsequent imposition of economic sanctions were part of America's efforts to counter Castro's alignment with the Soviet Union. There were also humanitarian concerns, as Castro's regime led to significant Cuban exile and internal dissent.
Step-by-step explanation:
Americans feared the takeover of Cuba by Fidel Castro because it represented a shift towards communism just ninety miles from the US mainland. This was significant due to the potential impact on national security, considering the historical priority of preventing rival nations, especially from the communist bloc, from gaining control in the Caribbean. The United States had previously tolerated the undemocratic rule of Fulgencio Batista as he opposed Communist movements, but Fidel Castro's ascent to power was seen as a move toward establishing a communist state allied with the Soviet Union.
The Bay of Pigs Invasion was a covert operation supported by the US with the goal of sparking an uprising against Castro's government. The failure of this invasion and the nationalization of US businesses in Cuba, along with Castro's military alignment with the Soviet Union, exacerbated fears and resulted in the US imposing economic sanctions and exploring other methods to counter Castro's regime. Cuba's alliance with the Soviet Union represented a direct challenge to the Monroe Doctrine and American hegemony in the Western Hemisphere.
Humanitarian concerns were also at play, with many Cubans going into exile and many others questioning whether they had replaced one authoritarian regime with another. The US response included sanctioning Cuba and plotting ways to undermine Castro's government to prevent the spread of communism in Latin America.