Back in Red Hood/Arsenal the duo was attacked by Duella Dent the self proclaimed Joker's Daughter. JD enjoyed what she did and what she did was usually gory. During a fight with JD Jason was strongly reminded of himself when he was lost and Batman helped him out. He thought that she must of felt conflicted about her actions since she didn't try to murder Roy and him. (*1)
Against everyone's warning Jason decided to mentor JD and enforce a no kill rule to set a good example for her. He wasn't however fooled by her act and doubted her sincerity throughout their supposed partnership. His suspicious were proven correct yet he couldn't kill her as he thought that would prove there was no hope for him. JD effectively got into his head to reinforce negative thoughts Jason already had about himself through the connection he saw between them.
The experience disheartened him by making him relive the helplessness of his own death and making him desperate to save Roy from the same fate. Disgusted that the people they were trying to protect wanted Roy's death for mere entertainment and forced to kill to save his friend Jason decided to break off their partnership. Claiming he wasn't a hero and didn't have the same faith in people Roy did.
What I love about this transition between the two series is how we see almost immediately how false his claims were. If Jason had no faith in people he wouldn't try to save anyone much less give others the chance to better themselves or work with him. Much like with JD a connection with a Superman clone is established right at their first meeting.
Only Jason is actually conscious during said meeting with the clone but he feels a kinship for someone else forced to live in a predecessor's shadow. In their next meeting during Bizarro's first time waking up Jason remembers the Lazarus Pit and how Talia Al Ghul feared him. Jason relates to Bizarro on different levels: Having to live up to someone else's legacy hence a feeling of loss of self. Not being sure of your place in the world or even if you should live in it. Being abandoned and rejected as Bizarro was supposed to be killed. And the burden of being a "monster." He also acknowledges the fact Bizarro is more than a lab experiment he's an innocent which JD never was. But just like with JD he wants to help Bizarro be a better person and also like her that belief is tested.
Other clones were more violent and Bizarro isn't quite aware enough to control himself yet. Jason let JD live and others suffered for it. His responsibility towards Bizarro makes Jason prepare to break his no kill agreement with Batman just to prevent future deaths. Bizarro is more sincere in his desire to be a good person and Jason finds himself unable to pull the trigger. The trust he gives is well earned as the clone proves he listens and Jason is honestly happy to be a good influence. When Bizarro dies fighting to save Artemis and him it upsets Jason so much he instantly suggests the Lazarus Pit to revive his friend.
Of course solicits spoil a little of the future plots and we know Bizarro will return which will bring another link between Jason and him. But Bizarro will apparently have his own ideas that don't mesh with what he was taught which will cause conflict. Will this force Jason to deal with the concept of killing Bizarro again?
*1 Jason probably believed this later on when he saw she went out of her way not to kill Roy. That made some logical sense although JD isn't a person that works on logic. Jason was better than JD but probably convinced himself that she was pulling her punches earlier when he connects her to his past experiences.