Supposedly, you have a man that's seen it all, done it all, etc. He'a smuggler, someone hard to trust. Naturally, if he has a gun in his face, he's going to know how it ends, so he takes action. Having him shoot first say this guy is on his toes, he's dangerous, can Ben and Luke trust him. It helps make his redemption a bit stronger at the end of the film. Now, he's a guy that can't see a shot coming from two feet away, and Greedo couldn't hit the broad side of a barn.