Yes it's self-defense, but Han shooting first gives him a harder edge that he's supposed to have, in order to complete his arc as >>6335
and as >>6339
said, the sequence shows that Han was subtly reaching for his gun, delaying and distracting Greedo until he could take a shot. Clearly the intent was there, so it makes no sense for Greedo to shoot first; you could almost say it "subverts expectations". It also reflects poorly on Greedo, who I think was a professional bounty hunter, not an amateur. If Greedo shoots first, and misses at point-blank range, that makes him seem like an ineffective retard, whereas with Han shooting first, he just got caught off guard by his quarry. And for Greedo to shoot right after confirms him as a serious challenge to Han, and his miss is understandable if he took a blaster bolt at the same time he squeezed the trigger.
While I'm on this topic, I remember reading Tales from the Mos Eisley Cantina, a compendium of short stories which varied but were generally pretty good. Greedo's story was a mixed bag -- I really dug the backstory with the clan wars, Navik the Red, all that shit was cool. However, I hated how they characterized Greedo as a newfag retard who got played for a fool, set up to die by his enemies. It just didn't fit the original scene, at all. If I decided canon, I would keep the clan/warlord backstory while ditching the rest.