Actually Han didn't shoot Greedo in self defense in the original version. He just shoots Greedo because he has to get to DB 94. Greedo is trying to get him to Jabba to pay a debt, killing him would only be necessary if Han tries to escape.
That's why GL changed it later. He said he didn't want Han to be a cold blooded killer. Which he is for killing Greedo like that. The SE changes actually make Han's character make more sense. If Han is the kind of guy to shoot first and not care, then why help the Rebels? Why not kill ewoks? Why come back to help Luke at the end of ANH?
All kinds of stuff gets thrown out if Han is the kind of guy who kills without hesitation. Han isn't a bad guy, so GL changed the one scene that made him look that way. Kudos George.
I still love the meme though. I'm all for the 2nd Amendment. :)