Kyouko is Tooru's mother.
As a young woman, Kyouko was a delinquent—she skipped school, got into fights, and eventually led an all-female gang. She earned the nickname "The Red Butterfly" from the way her motorcycle's tail lights looked dancing red in the night sky when she rode. Her own family rejected her, seeing her as a burden and caring only about appearances. By her own account, she hated them for it.
Everything changed when she met Katsuya Honda, a student teacher who actually stood by her. After her gang beat her down and her parents disowned her, he proposed. They married quickly and had Tooru. Katsuya became the stabilizing force in her life—someone who helped her work through her problems instead of abandoning her. When he died of illness, though, Kyouko fell apart. She neglected Tooru and sank into a depression so deep she nearly threw herself into the ocean, thinking she could join him in death. She'd never seen the ocean before Katsuya took her there, and it became tied to that memory of him. But at the last moment, she saw a mother and daughter together on the beach, and the image shocked her back to reality. She went home to find little Tooru waiting at the door for her—the same way Katsuya used to greet her. That's when everything shifted. She made a promise to never neglect Tooru again, no matter what, and she kept it. She raised Tooru alone and became something of a second mother to her daughter's best friends, Arisa Uotani and Saki Hanajima, as well.
When Tooru went missing as a young child, Kyouko lost it—she even threatened the police if they didn't find her. Yuki Souma eventually brought Tooru home after hearing Kyouko's frantic description of her, and Kyouko's relief was immediate and overwhelming.
Content compiled by AnimeList.moe from publicly available sources.