I don't know who, or why, it was done.
I suspect, however, that Lee Oswald wasn't a single shooter. There are too many bullet holes to account for.
According to the Warren Commission, three shots were fired, all from Oswald's rifle. The first was said to have clipped a tree. The second was the "magic bullet" that traveled through Kennedy, through Connally, and ultimately was found on Connally's stretcher (having broken his ribs, his wrist and then bounced into his thigh).
The third was the "kill shot" that struck Kennedy in the back of the head.
All well and good, save for the fact that it doesn't account for all of the bullet damage. Photos in evidence in the WC report show a crack on the inside of the limo's windshield. A pedestrian near the triple overpass was also hit by a bullet fragment.
According to Vincent Bugliosi's huge tome on the assassination, both the windshield ding and the scratched pedestrian came from fragments from the kill shot.
Bugliosi is a poor ballistician, in my view. As someone with a pretty advanced knowledge of firearms, I can pretty much state that among the bullets in a single box of bullets, all bullets pretty much share the same properties. That is to say, they're nearly identical and perform in nearly identical ways.
To accept the WC report we have to believe that a bullet went through Kennedy's neck, essentially spun, or "yawed" or "buzzed" through Connally causing all his wounds, and then ended up, only slightly flattened laterally, on Conally's stretcher. The very next round from the same rifle and from the same box of shells supposedly hit Kennedy, and instead of displaying the incredible strength and integrity of the first bullet, it essentially exploded. It caused the massive head wound to Kennedy, and dispersed into fragments large and fast enough to chip a car windshield and to travel 50 yards further down range to break skin on a person's face.
All of this is unlikely enough, but then there's the testimony of the doctors at Parkland Hospital, who described a bullet wound "approximately 5 mm in diameter" where they placed the tracheotomy. The Warren Commission/Bugliosi both state that this wound was caused by yet another fragment from the kill shot (it isn't accounted for by the other wounds).
In short there's just plain too many holes for the number of rounds fired. Something other than LHO acting alone had to be going on.