The whole thing was a sham from the get-go. The evidence that lone nutters love to throw around like gospel - "oh, a bullet can definitely hit one of the hardest bones in the body and come out pristine"; and "oh, of course a bullet can go through the neck [back with no termination point] and zig-zag on...of course"; and "oh, of course someone can pull off all of those shots with a creaky bolt-action with a misaligned scope, of course;" is actually quite hilarious.
Oswald had no motive - at all - to do what he did. He had actually claimed that he liked Kennedy. So there's that.