Oliver Queen killed a lot of people during his time as the titular vigilante on Arrow but it was his murder of a serial killer that was his most unjust. The Arrowverse's first hero did whatever it took to keep Star City safe throughout his stint as the Emerald Archer, but some of his earlier actions were pretty extreme as he often put an arrow in those who wouldn't change their corrupt ways. Though many could at least understand his motivations, this particular instance of Oliver killing on Arrow felt more extreme than the others.
Arrow season 1, episode 18, "Salvation", was a harrowing installment that saw a serial killer known as The Savior kidnap and kill people he believed should be punished for their corruption. Not too dissimilar to the Arrow's vigilantism, the one major difference was that he broadcast his tortured victims' final moments on TV for all of Star City to see. The sheer barbaric nature of his crimes forced Oliver to abandon his long-term goal of rooting out the corrupt powerful (something he wasn't quite used to doing yet) so that he could save the city from immediate danger by stopping the heinous display of violence. And in the end, that's exactly what he did, sending an arrow into the back of the assailant just as he was about to kill Roy Harper.
The problem, however, stems from the fact that The Savior wasn't like the rest of Oliver Queen's victims - he was quite the opposite. His real name was Joseph Falk and he was a grieving widower whose wife was gunned down in a robbery. Of course, his decision to violently slay Star City residents that he deemed incapable of being saved was not the right way to channel that grief but, if anyone should have understood his motivations, it was Oliver - something the pair conversed over right before the vigilante killed Falk to save Roy. And yet, it doesn't feel like the Arrow truly understood Joseph.
The Savior's deeds were unquestionably evil but, like Oliver's dark reckoning on Star City, he was motivated by a misguided attempt to make the world a better place. The Arrow's failure to understand him and his decision to ultimately kill him instead of disarming him (when he had one very long opportunity to) is especially hypocritical when you look back to the previous episode, "The Huntress Returns", and how Oliver tried to convince everyone around him that Helena Bertinelli aka Huntress wasn't evil in spite of her willingness to kill. Yes, Helena was another character broken by loss and motivated by murder, but vengeance was the only thing on her mind. She didn't care about collateral damage and Oliver even found himself attempting to justify her actions because of his feelings for her.
However, with Joseph, he did the opposite, rebuking him and rightfully suggesting that killing people like Roy for their life choices would rob them of a chance to change. He's certainly not wrong and this is a difference between him and The Savior that actually holds up because Oliver maintained that he only killed when he felt his target was beyond redemption. However, there is a strange irony in the fact that he used these words when pleading with Joseph to spare Roy's life and then did the complete opposite seconds later when he killed him.
"Salvation" was one of Arrow's most compelling episodes but it's hard to explain Oliver's questionable actions here. Not only did he refuse to give Joseph the same chance he wanted him to give Roy, the future Green Arrow's decision to kill him after sparing some of the corrupt people on his list would suggest that the he believed callous hitmen and mob bosses aren't beyond redemption but that a victim of people like them was. And while Joseph certainly needed to be stopped, couldn't a man trained in hand-to-hand combat, stealth attacks and theatricality have apprehended him without having to take his life?