Many believed it was the CIA. Those who supported the 'Domino theory' really didn't want the US pulling out that soon so he had to go.
Kennedy's head goes up in response to a shot fired either front near side or directly in front of him.....while the JFK movie is both bullshit and entertaining..it got some aspects of the offcial ct's correct.
Why did they believe it was the CIA. Based on what evidence does it implicate the CIA?