Tanjiro was sent to a blank room by an unknown entity,this is where he met the past Muzan,but due to Tanjiro being an empath,he comforted Muzan and hugged him.Tanjiro became(kind of) friends with Past Muzan,And when the blank room send them back to their own timelines,Tanjiro went back to his old life,without knowing that the present Muzan knew and felt what he did to his past self.Muzan became obsessed with Tanjiro's warmth and kind gestures,He would do anything to feel that warmth again.