I'm not sure what you're asking, so I'll just fill you in on the situation as best I can, and if you knew all this already, my apologies.
The original Han Solo from Star Wars was not really a big thinker, and the line about having "a blaster at your side" was kind of him defined. He gets frustrated on the intercom, he shoots the intercom. Greedo is going to take him in, he blows him down without a second thought.
In the new version, Lucas changed many things, almost all of them for the worse, and one of them was having Greedo shoot at Han first, thus making Han shooting "self defense" as opposed to "murder". The problems with this were many, but in short:
1) Softening the character of Han offended some die-hard fans
2) Greedo's gun is clearly pointed at Han, at point blank range. When it goes off, Han doesn't dodge, the gun doesn't move, nothing like that. Instead, it just fires off to the side for some reason. The idea that he missed doesn't make any kind of sense.
- J