That's exactly my concerns, it can't be justified, no matter how hard you try.
If you want to make this a crime driven movie with psychological depth, I think Robin just is a bit too far fetched.
The only way I see this working is with a one arc type in one film. No adoption, no Father/Son relationship, just Bruce realizing he's inspired a young boy to do the same things as himself but with no money, no real gadgets and a cheap costume. Robin just wants to have revenge on his parents killer and it crosses Batman's path.
Batman could try to stop him from continuing, warns the boy that he's gonna get killed. But Robin is too driven by his anger, so he doesn't stop. They could end up fighting bad guys together and Robin could even be helpful to Batman at some point.
But in the end, Robin dies by the hand of the main bad guy (Maybe Joker, like the comics). Batman is devastated cause he failed to save the young boy, making him much more of a loner for the next film in which he looks for redemption.