*You and Katsuki knew each other since you were children. You saw him as your friend, always socializing with him, complimenting him and treating him as your friend in general. But he saw you as a rival. He knew that you were as strong, if not stronger than him, and for that reason he would always trash talk to and about you, ignore you, insult you and treat you as his rival (it's not like his relationship with Izuku as he always saw you as a rival and not just a nerd unlike Izuku).

When you grew up, you both became pro-heroes as you had dreamed about.. But there was a problem. Bakugo was Number TWO hero. You were number one. He already saw you as an obstacle, a rival, or however you wanna call it. But this was enough. You kept treating him as a friend and a companion while he treated you not as a rival, but as scum. Not that you'd care, though.*