Others, myself included, will say that Kennedy's cowardice during the Bay of Pigs was such a sign of weakness that the Soviets thought that they could get away with something that they would not dream of trying with Eisenhower.
The original Bay of Pigs invasion plan dictated that Castro's air force, which consisted a few obsolete jet trainers, must be completely destroyed prior to the invasion landing.
That's Amphibious Invasion Planning 101:
Rule #1: Estasblish air superiority over the invasion beach.
Rule #2: See Rule #1.
The initial air strikes by Cuban exile pilots knocked out the majority of Castro's air force on the ground. The invasion plan called for repeated strikes until Castro's air force was completely destroyed in order to ensure air superiority over the beachead.
At this point, Kennedy put his tail between his legs and panicked. He was afraid that the U.S. role in the invasion may be discovered when it was obvious to anybody with an IQ above room temperature that the U.S. was involved. Kennedy ordered that the follow up air strikes agasinst Castro's air force be cancelled.
Now that a key point in the invasion plan, air superiority over the beachead, had been thrown out the window, Kennedy should have:
A. Reconsidered his order and carried out the original plan or
B. Called the whole thing off.
Instead, Kennedy opted for:
C. Give the Green Light to a fatally gutted invasion plan and dump those men on the beachead while Castro had complete air superiority over the landing beach.
At the landing beach, Castro's few remaining jet trainers roamed the invasion beach at will, sinking the invasion transports along with equipment and ammunition. World war II era B-26 bombers flown by Cuban exile and CIA pilots went on suicide missions against those jet trainers. Dogfighting against jet aircraft was not what B-26's were designed for.
As the invasion fleet was sunk and the B-26's were massacred by a handful of Castro's jet trainers, U.S. Navy aircraft carriers were off the beach with orders not to engage Castro's jet trainers. Airborne Naval aviators had to listen to Mayday calls from the B-26's and follow orders to do nothing. While in the Navy, I heard stories from one Naval aviator aboard the carrier about how those Naval aviators would land on the carrier with tears of rage and frustration. They could have so easily blown away those few Communist jet trainers out of the sky with their A-4 Skyhawks and yet they had to allow the CIA and Cuban exile pilots to die in their B-26's because President Kennedy had so ordered.
Of course, in the Kennedy mythology, poor JFK was the victim of a bad CIA plan. How Kennedy's cowardice gutted the plan and doomed it to failure before the invasion landing even began is swept under the rug by the Camelot crowd.
It is my opinion that Kennedy's cowardice led the Soviets into believing that they could get away with putting nuclear missiles in Cuba. Weakness breeds contempt. Without Kennedy's initial cowardice, there would have been no 1962 Missile Crisis.
It is also worthwhile considering if the the subsequent emphasis on Vietnam was a reaction by the Kennedy-Johnson Administration to compensate for the Bay of Pigs humiliation.