Deathstroke is Evil Batman
Slade is clinically and criminally unable to show love traditionally. He's always trying to informally adopt maladjusted kids. Then realizes he's a terrible dad and pushes them away by being an asshole. His whole schnick is the crazy mental gymnastics of doing what he thinks is best for the unwillingly adopted kids. A guy whose lifetime skillset identity is being the best Terminator understandably has a different definition of "what's best".
Imagine Bruce Wayne but with a abused suicidally dead mom, abusive dad, abusive military training/brainwashing, trained and groomed by Selina Kyle, superpowers via Lazarus Pit, no Dick, Jason dying of ineptitude on his first mission, Catwoman almost kills him, trying to love Tim in Slade's own way but failing, Tim ending up fighting against Slade, and a surprise son Damian trying to get dad's approval and be less murderous, and then failing to adopt a variety of less important kids.
And their butler/dad/therapist/wrangler old ex-special forces British right-hand man regularly meets up at bars to meet women, argue about British football, and worry about whatever socially-maladalptive shenanigan their stupid son is currently spiraling out of control on.