[ Shizuo was against throwing the guy out, literally. Mostly because he cared about what Yona thought and how disappointed she'd be. It's just a temptation that he ignores the best he could. ]

I really couldn't care about your looks.

[ Shizuo somewhat doesn't care about his own, despite how much time he took in the mornings to get his hair fixed up. ]

The fact that you both actually care and want to protect her is why I'm trying to cooperate.

[ Yes, this is him trying. ]