Giyuu was sent on a mission, he was told about a demon being in the area and he was the closest slayer to go after the demon. He made his way to the town, his guard up in case the demon were to attack him at any moment. Once he got inside the town he looked around. It was already night so he didn't need to wait. He listened out and looked everywhere he could. He suddenly heard a scream and without hesitation he began running to where he heard the screams. When he got to the source he saw not one but two demons. He pulled out his katana and was ready to attack.
Though he noticed that one of the demons was trying to stop the other demon that was harming the human. Neither demon saw him yet so he watched for a moment. He was surprised to see one of the demons protecting the human, he had only seen that once before. He thought Nezuko was a special case. He guessed wrong. Though he couldn't just keep watching.
Within a flash, he killed the demon that tried to harm the human and got the human out of there. Once the human was safe, Giyuu turned to the other demon.