IIRC the CIA and other parties were upset Kennedy didn’t commit further to the invasion. Kennedy’s refusal to provide direct air support after the CIA backed forces lost the initiative is usually cited as a major point of contention.

More conspiratorial theorists like to speculate that the CIA hoped to lure the US into a full-scale invasion of Cuba by escalating the Bay of Pigs invasion. By refusing to provide direct air support, Kennedy essentially stopped that from happening and doomed the invasion and ruined Allen Dulles’ reputation. I have no clue how valid these theories are, but it’s what’s usually cited.