Cuba changes the balance
Fidel Castro's revolutionary movement overthrew Fulgencio Batista in 1959. Relations with the United States deteriorated as the new government developed closer ties with the Soviet Union. To Washington, a communist ally of Moscow in the Caribbean presented a strategic and political challenge; to Havana, American hostility threatened the survival of the revolution.
In April 1961, a CIA-backed force of Cuban exiles landed at the Bay of Pigs. The invasion failed. Its consequences mattered in October: Cuban leaders had direct experience of an attempt to overthrow them.
Sources for this passage: [1]
An invasion feared, a covert campaign continuing
The failed invasion did not end American efforts against Castro. Operation Mongoose organised covert action against his government. An October 1962 CIA memorandum discusses infiltration, intelligence gathering and sabotage. Cuban fears of further attack therefore had a basis beyond Soviet propaganda.
The United States and Cuba also contained sharply divided communities. Exiles who opposed Castro and Cubans defending the revolution understood the danger very differently. Neither government spoke for every Cuban.
Sources for this passage: [2] [1]The Soviet gamble
Khrushchev authorised a secret deployment to Cuba, codenamed Operation Anadyr. Its purposes included defending a new ally and improving the Soviet strategic position against the United States. It brought troops, air defences and nuclear weapons across the Atlantic.
American nuclear weapons already threatened the Soviet Union from Europe. Khrushchev later explicitly cited missiles in Britain, Italy and Turkey. That context helps explain the deployment without making the two sides' decisions, geography or alliance arrangements identical.
Sources for this passage: [3] [4]