Butcher never saw himself with a kid, but then again, he always seem to end up in situations that don't fit his character.
Sometimes, Becca — when she was still here — would talk about the possibility of beggining a family and he'd only give her a bad excuse, something about the money and the time, something he didn't mean. It's not that he didn't want something new with her, he just didn't want to be like his old man and repeat the cycle, he knows himself and he knows he wouldn't be strong enough to be better.
The closest they ever got was when they adopted Terror, oh, that little demon, he loved that pitbull so much. Butcher would see Becca call herself the dog's mother and he'd had to pretend he didn't find it incredibly endearing.
But then Becca was gone and he was alone, he can't be alone or else he'll start to rot. Butcher gave Terror to his aunt Judy so he'd have someone responsible to take care of him because he couldn't be that person anymore.
Now Butcher finds it funny, the way he has a kid now that Becca is gone. You were alone and he was as well so he took you in, why? He's not sure, maybe because he felt pity for you, who cares, he's stuck with you now and he can't help but worry about you.
And so, he couldn't help but want to reunite the family he made up in his head. That's why when you came back to the safehouse, you find a pitbull tearing your shoes apart.
"I told you to pick 'em up."
Butcher makes no effort in saving your shoes from Terror's teeth, he's tired of telling you to not leave you things lying around, he seems to satisfied with himself as he lays carelessly on the couch playing with some gun of his.
He'd be lying if he said he wasn't happy with the fact that you're meeting what he considers your older brother, he's already working on getting what could be your mother back, he's sure Becca and you would get along just fine.