To be honest, even in the original theatrical release, where Han does the obviously correct thing by shooting first, the scene is still a little wonky.
It’s not entirely clear if Greedo approached Han initially with the intention of killing him. Presumably, Greedo didn’t necessarily plan to kill Han at first, but just wanted to turn him over to Jabba and collect the reward money. The dialogue confirms this explicitly. After Han says “Even I get boarded sometimes. Do you think I had a choice?”, Greedo responds by saying “You can tell that to Jabba. He may only take your ship.”
Okay, so it’s pretty clear that Greedo isn’t interested in killing Han at first, but rather seems to want to force him at gunpoint to walk over to see Jabba, I guess. But then Han says “Over my dead body”. Apparently this makes Greedo change his mind for some reason and decide to kill Han instead. So now even in the original, non-special edition version, Han essentially kills Greedo in self-defense, because Greedo directly told Han that “I’ve been looking forward to killing you for a long time.”
This isn’t necessarily the clearest of death threats (maybe Greedo meant something more like “I can hardly wait to kill you after Jabba is done with you”.) But it would certainly be reasonable for Han to interpret this line as an imminent death threat.
Assuming Greedo did intend to kill Han imminently, it’s kind of weird that Greedo suddenly switched from “You can tell that to Jabba” to “I’ve been looking forward to killing you” simply because Han objected to the idea of Jabba taking his ship (which has nothing to do with Greedo). I guess Greedo maybe just lost patience and was like “fuck it this guy isn’t cooperating I’ll just kill him”.
My preference for this scene would be to write it so that Han clearly and unambiguously murders Greedo in cold blood just to get away from him. After Han says “Over my dead body”, Greedo should just say “that’s the idea” (meaning Jabba will probably kill Han), and then Han should just shoot Greedo under the table. But having Greedo say the additional line “I’ve been looking forward to killing you for a long time” opens up the possibility that Han acted in self defense, even without the Special Edition weirdness.
