Why might Kennedy have wanted to cover up American involvement in the invasion? Why did he choose the Bay of Pigs as the landing site?

Before his inauguration, John F. Kennedy was briefed on a plan by the Central Intelligence Agency (CIA) developed during the Eisenhower administration to train Cuban exiles for an invasion of their homeland. The plan anticipated that the Cuban people and elements of the Cuban military would support the invasion. The ultimate goal was the overthrow of Castro and the establishment of a non-communist government friendly to the United States.