One reason why I think the first arc of Batman and Robin 2011 worked so well is because the new villain, Morgan Ducard, son of one of Bruce's teachers when he trained to become Batman, was designed to develope Bruce and Damian as individuals but also as father and son.
Morgan acts as a rival to Bruce for the position as Damian's father and teacher because Morgan wants to get revenge on Bruce for beating him up so badly in front of his father back in their training days that Henri Ducard disowned Morgan. In his eyes Bruce stole his father from him, so he is going to steal Bruce's son.
Bruce doesn't want Damian to help him with Morgan because he is worried about Morgan hurting Damian and all that stuff, but also because he doesn't want to admit to Damian that the rage that Damian feels inside is something Bruce also suffers from and that it lead to him almost killing Morgan when he beat him up years ago. Because Damian knows that Bruce is hiding something from him he feels like Bruce doesn't trust him and the two argue.
Morgon uses this and tries to manipulate Damian to join his side and it forces Damian to think about his own feelings towards killing and about his relationship with Bruce.
When Morgan discovers that Damian had been playing him the entire time and had no intention to actually betray Bruce Morgan wants to torture and kill Damian while Bruce has to listen to it to get revenge, which enrages Bruce so much that he almost kills Morgan by pushing him into acid. He only stops when he realizes that Damian is watching him, causing him to come back to his senses.
Morgan taunts Damian by threatening to kill Damian's family and Damian kills him to prevent him from doing that (Morgan is actually a very dangerous villain, Damian saw him almost kill Bruce twice, just for context)
Bruce carries a badly injured Damian off the sinking boat they are on and urges Alfred to take care of Damian instead of him even though Bruce is also in such a bad state that he falls unconscious shortly after handing over Damian to Alfred.
The whole ordeal leads Bruce to open up to Damian about his own rage and bloodlust and they manage to have a talk about it at eye-level instead of Bruce just preaching about it from a place of superiority.
Morgan was a cool villain on his own, but he doesn't just show up because the creative team of the book had a cool idea for a new character they wanted to push somewhere, his main purpose was to push Bruce and Damian's story forward and he did that very well.
