Of course Han shots first, he's an Anti-hero and it is only logical that he shot first.
People tried to justify him shooting Greedo out of self defense, but he is Han Effing Solo.
Like he gives a shit about being on the up and up.
He is a smuggler, a wanted criminal (by both the Empire and seedy underworld kingpins), and an all round nogoodnick who looks out for only himself and Chewy.
Even throughout the trilogy he only really does anything for the rebellion because he is fiercely loyal to Luke and wants to bone Leia.
Those things only even came to be because Luke lured him into helping rescue Princess Leia by reminding him that she is royalty and therefore rich, which would land him a handsome payoff for rescuing her.
He shot first because he does what he pleases and has no problem killing a scumbag who fully intends to murder him.