Being the Eye of Twilight requires someone to not allow emotions to clog there judgement. It's not that he doesn't have any, just that he's containing them to maintain the balance as shown in one of his stories, I can't remember the title but he kills a priest because he was hunting demons.
But when it comes to Zed/Jhin he obviously has a hard time containing these emotions. He has to work with Zed to kill Jhin, because he knows that He can't do it by himself, but really wants to end Zed because he killed his Dad. I feel like his anger toward Jhin is more than his towards Zed, as Jhin basically ruined both of their lives with all the shit they saw.