One: when Ravager tells Batman she'll tell him where Robin is if he helps them, he just jumps from the roof and says No. Lost boys are a dime a dozen. I'll just get another one.
Two: As Robin and Deathstroke are lazily sort of pretending to try to get into each other's head (while the latter is "watching" the former "drown" (it's all very Xanatos)) and Slade wonders what the League of Assassins did to Damian, he answers Oh... You wanna be my dad now?! Fine -- And then he *exposes his throat to the camera, smiles the most most psychopathic smile you could imagine, and says* -- Come on in here and slash my neck. Then I can be your kid, too.
The first time I saw it, my reaction was a silent but heartfelt emotion that can best be expressed by the nearly-mystical term Dude.
My takeaways are that 1. Bruce was obviously playing to Rose's psychological issues, 2. he's a very emotion-driven man who can also be almost psychopathically disciplined when he thinks it's the right call, and 3. Bruce has nothing on Damian's unbridled psychological savagery. Bruce grew up a nice person (with, I postulate, underlying issues), got hurt, and trained himself into somebody capable of violence. Damian was hurt from day zero, and was trained all of his life for violence of every kind. He had to figure out and learn how to express kindness and caring — every animal he saves is a Fuck You to his entire upbringing — because he grew up being taught otherwise.
Damian was abused by most definitions of the term. It's not cool, it's not nice, it didn't make him a better person. He speaks interpersonal brutality — the deliberate, forceful establishing of hierarchy — with the same unconscious fluency than Cass speaks hand-to-hand violence, and for similar reasons, and although both of them have gotten much better at communicating in other ways, it's still their mother tongue.
Anyway. I'm, as usual, overthinking a couple of lines of dialogue. The short version is that Damian was raised with a very unique "operating system" for interpersonal interactions, one that's very painful and unhealthy, and that has as a minor and totally-not-worth-it side effect his capacity to be brutal in ways that, say, Jason could never be.