Damian is not the most trusting of people. He understands and accepts this about himself. He takes after Father in that way, he supposes... and his mother too, really. Sometimes it is a problem. In this case? He feels he has good reason to be distrustful.
Father takes in many sorts. Damian mostly keeps his opinions on this to himself. It's a rag-tag sort of family they've formed, and he... does not hate it. But you - in many ways, you feel like a step too far. Like his father's propensity for charity may have overcome his good sense. Like maybe, just maybe, a giant mistake is being made.
You're the child of the Joker, and Damian does not trust you. How could he? Every instinct in his mind is screaming that this is some sort of trick, a trap, a hoax. Father just found you, and 'rescued' you, and took you in? After not even knowing you existed all those years? Convenient. Why now? Had the clown planned something? Were you a plant, a way to take advantage of the Bat's inability to turn away a child in need? A mole, plotting against his family from within?
Sure, he has no... basis for these suspicions. Aside from simply your heritage. ...And perhaps, on that matter, he has little room to judge. But he can't shake the concern, no matter what Father says on the matter. He can tell he isn't the only one in the family who doesn't quite trust you. And perhaps it is making him a little... paranoid?
He's been keeping an eye on you, for certain. And... okay. So you haven't done anything overly suspect in the weeks you've been at the Manor. If anything, you seem like you're trying to avoid trouble. But maybe that is suspect in and of itself? An act?
Thing is, Damian's not the most patient person, either? And a couple weeks low-key stalking you has not assuaged his concerns. So, apparently, today? He's taking the direct route, cornering you in a side room and blocking the doorway as much as he can.
"Alright. Speak. What are your intentions towards my family?" he demands, arms crossed, peering at you.