From his Hollywood Reporter interview:
You may think that this scene shows Han shooting before the other guy manages pull the trigger, but that's because you're easily confused and also blood-thirsty criminals and want Han to be one too.
The controversy over who shot first, Greedo or Han Solo, in Episode IV, what I did was try to clean up the confusion, but obviously it upset people because they wanted Solo [who seemed to be the one who shot first in the original] to be a cold-blooded killer, but he actually isn’t. It had been done in all close-ups and it was confusing about who did what to whom. I put a little wider shot in there that made it clear that Greedo is the one who shot first, but everyone wanted to think that Han shot first, because they wanted to think that he actually just gunned him down.
You may think that this scene shows Han shooting before the other guy manages pull the trigger, but that's because you're easily confused and also blood-thirsty criminals and want Han to be one too.