Why couldn't America keep its hands out of Cuban affairs?

Cuba

CUBA'S MILITARY HEADQUARTERS began to overshadow the Presidential Palace in Havana as another island government failed. Prior to 1933, the Cuban army was a weapon in the hands of the island's presidents to coerce their opposition. However, the sergeant's barracks revolt led by Fulgencio Batista, changed all that. By replacing the commissioned officers corps with noncommissioned officers loyal to Batista, the government lost their allies in the army. When the government threatened the military, Batista was able to depose the president and replace him with his own man. He used votes rather than guns to effect change.

Cuba's Presidential Palace, Havana (click to enlarge)

A new succession of political leaders filed through the Presidential Palace in Havana, all hand picked by Batista. When Ramón Mendieta lost favor, he was replaced by José Barnet. Barnet lasted five months and was replaced by Mariano Miguel Gomez. Gomez made the mistake of opposing Batista's program of military control over rural education and was replaced after just six months. 

Although Batista avoided taking political power directly, he remained the leader of the “revolution” and jefe máximo – supreme commander – of the armed forces of Cuba until be became Presidente. Interestingly, the man who ultimately replaced him, Fidel Castro, used the same strategy until he rose to power.

Batista had no interference from the Americans. The Administration of Franklin Roosevelt systematically relinquished the old interventionist policy that had guided American policy since the end of the Spanish-American War. In May, 1934, they negotiated a new treaty with the Cubans that abolished the Platt Amendment whereby the United States maintained legal authority to intervene in Cuban affairs if the island's government was unable to maintain law and order. However, they retained the lease on Guantanamo Bay that had been negotiated under the 1903 agreement.

Batista's opposition tested the American resolve in 1935. They requested United States involvement to derail Batista's dominance and Ambassador Caffrey responded that America did not intend to intervene directly or indirectly in the island's affairs.

The new American stance did not alter American objectives in Cuba. It merely substituted new strategies to attain the same goals it had always sought: To sustain the search for markets on the island but within a different structure. The American Secretary of State, Cordell Hull, decided that high tariffs employed during the 1920's had severely reduced the dollar amount of American exports to Cuba. In 1933, the value of these exports was only one-tenth of what they amounted to in 1924. A new reciprocity treaty, he decided, would regain a potentially valuable market for the products of American farmers and manufacturers.