He may have kept his cool during the missile crisis, but that was caused by his Bay of pigs invasion, which was an unmitigated disaster.
President Dwight D. Eisenhower was the one to initially authorize the CIA to recruit 1,400 Cuban exiles living in Miami and begin training them to overthrow Castro in 1960. However, due to the nature of the Cold War and the very real threat to the democratic West, and of course especially the USA, President Kennedy liked the plan when he came to office in January 1961. It was foolishly enacted with the known results!
When looking at the history of the time we must consider the context in which political decisions were made, and in this case the magnitude of the perceived, and very real threat, that the Soviet Union posed to USA and western allies interests after 1945. It had been just 10 years since the Soviet and Chinese backed North Korea had invaded the South in 1950, and after 3 years 300,000 had been killed. The Berlin Wall had been erected in 1961, and after the Americans successfully put into service a ballistic missile system in 1959, the USA was shocked to find the Soviets were trying to place their own ballistic system into Cuba, within the US backyard, in 1962 after that country had gone communist. Then you have the threat of spreading communism in Indochina,when in 1954, Viet Minh won a crucial battle which ended French dominance in Vietnam, and a year later, in 1955, the "unofficial" USA involvement in the Vietnam War started, only ending in a humiliating defeat for America in 1975.
So any American President heading the USA in those difficult times had to make some very difficult decisions, and, yes, with the assistance of the CIA could cock it all up! If anything we can thank our lucky stars that once the USA ballistic system came into use, there was no need for B52's of the US Strategic Air Command (SAC) to be patrolling 24/7 along the Soviet border, awaiting the crucial signals from a distant President to "send them in" for nuclear strikes, along with the British V Force. After 1959 all the President's had to do was press buttons to send the missiles up!! Of course the Soviets would have mirrored all that and Armageddon would have been complete!!