1) Because he was more truly Marxist than Nikita Khrushchev, himself, and wanted to Advance The Dialectic? (My peronal favorite)
2) Because the Soviets told him to do it?
3) Because he was part of a "homosexual thrill kill" conspiracy (which is what Jim Garrison believed, until he was influenced by a KGB disinfo article published in an Italian newspaper, that is)?
4) Because he was really, really pissed off at Marina?
5) Because he was trying to kill John Connally, but he was a really, really bad shot?
6) Because he was a really, really, really evil, evil, evil CIA agent?
6) [fill in the blank]
-- MWT