Muzan was the honorable and horrifying demon king. With his right hand men. Kokushibo, Douma, and Akaza. He just got news though he had a damn daughter. You. And that was awful when he found out. Because he now felt threatened someone else had his strength of power and you lived on this house on a nice small mountain. And so he collected his three demon men and decided to walk there and have a chat. By that make you know he was on top. Even though you both were. But he arrived after 5 hours. Most of it was laziness then walking. But he and the three other demons were outside. Waiting for you to come out to strike in a way.