Because the CIA is the evilest of evil doers. CIA controls everything and everyone, and it's his job to point this out because the JFK assassination "changed everything".
The problem is that the scenario he embraces not only does not work operationally, and is not supported by the sober evidence, and is not reflective of how operated in 1963.
I keep telling people that Oswald left enough dark corners in his life between 1962 and 1963 that could offer hope for conspiracy theorists. The problem is that it's nothing sexy like multiple gunmen in Dealey Plaza, and a massive government coverup carrier across multiple government and state agencies.
Right now there is a CIA memo from the last document dump from the Mexico City Station advising Langley to pass along information that Oswald had visited both the Soviet and Cuban embassies to the FBI, and that the FBI take a closer look at him. That information was never passed from Langley to the FBI...I think this is as close as CTists can ever get.