Perhaps Greedo just slipped his finger over the trigger. He didn't want to kill Solo. Unfortunally GL cut a scene that was supposed to go between Greedo's shot and Solo's shot:

"Woops sorry slipped my finger, happens all the time. Let me put this gun away. What was I saying? Oh yes... I've waited so long for this moment... Solo... I... I can't hide it anymore. I'm secretly in love with you. Here, I'll pay all your debts with Jabba... Let's run away together! I know a little place in Naboo where we won't be found... And we can make love together from the sunrise to the sunset... Please..."

Solo shoots Greedo.