This is what George Lucas says about Greedo shooting first in a 2012 interview with "The Hollywood Reporter":
"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 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."
Here is how the scene was described in the 1976 book "Star Wars: From the Adventures of Luke Skywalker", where Greedo is referred to as "the unctuous alien" and "the creature":
“Light and noise filled the little corner of the cantina, and when it had faded, all that remained of the unctuous alien was a smoking, slimy spot on the stone floor.
Solo brought his hand and the smoking weapon it held out from beneath the table, drawing bemused stares from several of the cantina’s patrons and chuckling sounds from its more knowledgeable ones. They had known the creature had committed its fatal mistake in allowing Solo the chance to get his hands under cover”.
So Lucas claims that Greedo always shot first, but it doesn't really sound that way in the book. Also, Lucas thinks that what the fans want is for Han to be a "cold blooded killer", which shows that Lucas misunderstands where the fans are coming from. The following is copied and pasted from swtor.com, it's a post on there by a fan named "AcousticColors" who sums up George's misunderstanding better than I can:
"nobody believes shooting somebody with a gun pointed at you who just told you that they could arrange to have something taken over your dead body makes you a cold blooded killer. That's called self defense.
So, let's look at the scenario...
The way the fans want it...
Greedo sits two feet from Han... Han realizes Greedo is about to squeeze off a bolt, and at this range, there's no way he could miss, so Han preemptively pulls out his own blaster under the table and fires first, the shot hits, causing Greedo's aim to veer and hit the wall near Han's head.
The way Lucas wants it...
Greedo sits two feet from Han... Han realizes Greedo is about to squeeze off a bolt and pulls his own blaster out under the table. Even so, Han sits there and lets a shot get off, counting on the fact that this bounty hunter has such horrible, horrible aim that he can't hit a large, non-moving target that's sitting two feet away. Han's incredibly stupid gamble pays off, Greedo does in fact miss the broad side of a barn, and then Han shoots him.
Which of those is the better story? It's not about wanting Han to be a cold blooded killer, it's about not wanting Greedo to be such a worthless Bounty Hunter that he can't hit somebody sitting right in front of him, and not wanting Han to be an idiot who just sat there and let himself get shot at from near point blank range."