Inuyasha had grown up thinking Inutaisho was his father and Izayoi was his mother. He believed it too that was until he went with Souta and Kashu to the history museum. Kashu, Kagome's mother, was chaperoning a field trip for her son Souta's class and had thought Inuyasha would enjoy going and Souta would enjoy having him there. That and she could use his sharp hearing and great sense of smell to keep track of the kids in their group.
