Well, that's one of the arguments for "Han Shoots First" I've heard over the years but the bigger one, the one I usually go with, is just that Han is a ruthless smuggler sitting three-feet away from a bounty hunter who has just said he's after Han's head. Why WOULDN'T Han shoot first? The change also is problematic for several other reasons for me:
1. The "idea" of the Special Editions was for Lucas to go back and add or fix things he wanted but couldn't do back in the 70s/80s. Things like other creatures, more extras/troopers, making planets look more alien or otherworldly, removing matte lines and the like. So what in 1977 prevented Lucas from being able to film Greedo shooting first and Han dodging the shot?
2. It makes Greedo look like the galaxy's worst shot considering he missed a man sitting three-feet away from him (point-blank range) with a LASER!
3. Han DODGES a laser. Say what you want about the EU suggesting Han has a degree of force-sensitivity that gives him what he calls "luck" that's a pretty damn hard stunt to pull off. A laser (and even if we assume it's literally not light but a particle of some sort it's still going be traveling at very close to the speed of light like electrons do) is going to get from Greedo's gun to Han's head in like a couple of femtoseconds.
The change was just pure dumb. The "arc" of Han's character is a good argument if you don't want to completely buy into Han being a ruthless killer unless there's a "means to an end" for him to be so. But that doesn't change the "fact" of what's going on in this universe. Han IS a scoundrel and he'd hardly be a ruthless killer for taking down a man with a gun who's sitting three feet away from him who has JUST SAID he's going to kill him.
Ugh... Breathe.... Breathe.... "You're not even *that* big of a Star Wars fan."... Breathe... Breathe... Relax, think of Kari in the Endor Camo.... Relax....