I should clarify: I have no problem understanding why it is more logical for Han to shoot first, why it fits better with the facts of the scene. What I couldn't understand was the emotion fans invested in it, the way they seemed to celebrate and glorify the act of shooting first as if it were somehow heroic or admirable, which seems morally backwards to me. But Adam's explanation makes far more emotional and ethical sense to me -- that it's not about glorifying the act of violence, but about valuing its role in Han's emotional journey from scoundrel to hero. It's about the contrast between the ruthlessness of that act and the compassion and selflessness he develops later on. That's something I can actually understand getting emotional about.
Or that it was just incredibly cool that he didn't give a fuck and shot first.