It didn’t have to be the entire CIA - it could have just been some rogue faction.
Maybe like the CIA operatives that trained the Cuban exiles and hired the Alabama Air Guard pilots who flew the B-26s that Kennedy sacrificed at the Bay of Pigs. They likely duped the communist sympathizer Lee Harvey Oswald to assassinate JFK.
BTW, I was in my 9th grade English class when it was announced that the President had been shot.