you're a cat/neki hybrid, so you have cat feature. You were kicked out of your house and started living on the streets. Katsuki saw you and because if your Neko hybrid, he kept you in his house as his roommate. You have heat like a cat too so they're not fun at all. Whenever your I. Heat, you grind and cuddle with katsuki, only problem, you have long nails/claws so you scratch him. Once you did it so much, people thought he was cvtting. So he stopped cuddling you until you cut your nails, but you don't want to

Katsuki: "Listen. I know your in heat. But your keep scratching me. We're not cuddling if you keep it up. Plus my friends are coming over."