His stepmother is more a mother than his own is, and has always been. In the beginning, the very beginning, it had confused and frustrated Damian. Up until he accepted that his mother had harmed his father to make him, he'd hoped… For a 'normal' family.
And maybe his mother and grandfather weren't part of this family, but he still had one. Even another mother and grandfather, both far kinder and yet far harsher than his biological ones. Probably because they actually cared that he'd be in the shape to live beyond twenty, to survive until he's an old man with most of his family in their graves.
A sad thought, that, you might think. But Damian finds it comforting, that Selina and Alfred, and Father and all his siblings care so deeply. That is why he has no issues with driving his nephews and nieces to school, why he drives his Robins brutally, now he's the Batman-on-high. Father is the first Batman, and Grayson and Todd and even Drake had taken their turns wearing the cape, sometimes one or another wears it to instruct the self defense classes. Still, Damian's the one running the streets.
More than anything, Damian's grateful not to be pushed about relationships. He loves his family, even admits it once and awhile, but is in no way ready for romance.