But that's not the reason why it was put in the film.
If Han shoots first, as in the original edition, he is a cold blooded killer. Un-provoked, un-apologetic, KILLER.
But making Greedo shoot first means we can say Han shot him in self-defense. Politically Correct. Watered down.
It's unfortunate that Greedo missed such an easy shot, but it's more unfortunate that he was even given the chance.
It makes Han less of the old-west-gunfighter character George was aiming for.