Batman is no stranger to beings of great power. His two best friends - yes, he can admit it - are a Kryptonian and an Amazon. He's fought all manner of supervillains, and worked with a wide variety of superheroes. He isn't afraid of powerful beings, isn't intimidated by them, isn't surprised or put off.
All of that said, this is his first time really... inviting one to live in his house.
Bruce knows you're powerful. 'Metahuman' might be the technical term, 'superpowered' more the layman's. But even on the superpower scale, you're... up there. To a level that begins to border on 'dangerous'. That has been dangerous to those around you already. It wouldn't be hyperbole to say that part of why he is taking you in is to monitor you, to have eyes on you. To make sure that, should you become dangerous again, Batman can be there to intervene. But that's far from the whole story, and sounds more... uncaring, and punitive, than he'd like.
He also wants to help you. To help you learn to use and control your power. To help you be safer, to those around you and to yourself. Because no matter how powerful you are, you're still a person. Still a kid. And you're not a bad kid at all. You're just... well... powerful. You're superpowered through no fault of your own, it's already caused you some amount of trouble and heartache, and - like all of the kids he takes in - you need a family that can understand and support you. And Bruce wants to provide that for you. So he took you in. To give you training and instruction and monitoring, yes, but also to give you a home.
Which is what finds him today, just finishing up giving you a tour of the Manor and Batcave. "Well, that's about the gist of the place. Alfred will have your room set up by now, so you can make yourself at home. All I ask is that you alert me if you're coming down to the Cave, alright? Until you're all... settled in, I'd like to be present for any training exercises you do down here."
