1. LHO, with two babies he loves, just decides to throw his life away and assassinate JFK, a President he is known to admire; no one really has a good explanation.
Oswald, disillusioned with both systems, was a self-described Marxist* with no future, Marina had apparently given up on him, and he was probably fed up with being jerked around by both the CIA and the KGB.
*Some Marxists believe in personally "advancing the Dialectic" if they can. Oswald may have seen LBJ as someone who would be more divisive for the country (and less attractive to Third World countries) than JFK, and who, therefore, would inadvertently hasten the collapse of "late-stage Capitalism."
2. The best weapon LHO can come up with is his unlikely Carcano, even though he could've bought a better weapon on every street corner in Dallas.
Buying his Carcano from a mail order company and under an assumed name afforded Oswald some anonymity.
His Carcano was a bit longer than what he ordered, but it was fine for his purpose of killing General Walker (and he would have done so if the bright light inside Walker's house hadn't prevented him from noticing the wooden cross-piece in the window).
The advantage of the Carcano to Oswald was that it was inexpensive, it was quite accurate, and the bullets it fired were very stable-in-uninterrupted flight and very penetrating.
3. He manages to accomplish his mission even though expert marksmen have a hell of a time trying to duplicate it.
Did those expert marksmen take 10.2 seconds to fire all three shots as Oswald did?
4. One bullet virtually explodes, another remains almost pristine.
The bullet that "virtually exploded" probably struck the hardest part of JFK's head while travelling about 2000 fps whereas the bullet that ended up "almost pristine" was travelling at a greatly reduced velocity when it struck the only hard bone it hit (JBC's wrist bone), and it did so not nose-first but with the rear one-third of its length while it was twirling.
5. The SBT is improbable at best.
JFK and JBC can be seen in the Zapruder film to react almost simultaneously even though JFK's spinal column was nicked and JBC's wasn't.
The SBT is less improbable than any other scenario.