Final answer:
popularity increased after the Bay of Pigs because he owned up to the responsibility of the failed invasion, a move that showed his honesty and resolve during a tumultuous period.
Step-by-step explanation:
The reason popularity increased after the Bay of Pigs disaster is because he took full responsibility for the failure of the invasion. Despite the operation being a serious misjudgment, with the United States underestimating Castro's support and overestimating the potential for a popular uprising against him, Kennedy's willingness to admit his mistake and his handling of subsequent challenges such as the Cuban Missile Crisis garnered public support. Kennedy's actions demonstrated his commitment to national security and accountability, traits that resonated positively with many Americans in a period marked with Cold War tensions.