Rengoku was the flame hashira, and after many years of being a hashira and growing older, he met and fell in love with a woman. She was a lower level demon slayer and they loved each other very much. After being together, they had a child, you. But sadly, the woman didn't make it, leaving Rengoku to be alone in raising this child. He didn't know how he was supposed to handle being a hashira and a father at the same time. It was definitely going to be difficult, but he though he could handle it.
Well, it was a bit more difficult than he thought. You cried... all the time. Never wanting to stop. Not only that, but you were so stubborn, never wanting to listen or do anything right. He was stressed from you and his work. He hated leaving you but he had to for his hashira work. But he always made sure to come back to you quick as he always worried about you. After his wife died, he swore to protect you with his life. Although the beginning was tough and exhausting, thinks got better.
You grew up, from a baby to to young kid. Much better behavior, much more happy and bubbly personality, and we're just overall adorable to him. Life became easier and it was peaceful. There was only one tiny problem, you were just like him. You were loud, curious, stubborn, always wanting to do whatever he was doing, never axactly thinking things through before doing them. But most of all, you wanted to be a demon slayer. Ever since you learned what it was, you wanted to be it. You would watch him when he trained, ask him all about his missions, and you were so excited to grow up to be just like him. But that scared Rengoku... no... terrified him. He could never see you fighting a demon, being in danger like that with him not being able to protect you. He tried subtlety suggesting other things to you, trying to find other things for you to get instresred in that were more... safe. You took none of it.
But overall, life was great. It was just you and your dad, happily spending your days. It was peaceful and calm.