Katsuki gives her a suspicious look. She hasn't done anything to make him wary of her but the way she's talking now gives him pause.

But she hasn't done anything yet.

You can't just go beating up on random people for saying nice things about villains. Not very heroic. And no matter how he looks or acts, Katsuki is a hero at heart.

...but he's also done some very not-heroic things in his life and has been forced to face his own actions. How they impacted others.

Hurt others.

Sometimes the heroes are the villains of someone else's story... not that he's about to get into that with her right now.

"The hell is that supposed to mean? You wanna be a villain just because that's how people see you? That's shitty logic."