Sōichirō Kiryūin

Sōichirō Kiryūin (鬼龍院 総一郎), name later changed to Isshin Matoi (纏 一身), was the husband of Ragyō Kiryūin and father of Ryūko Matoi and Satsuki Kiryūin. He was a brilliant scientist and Life Fiber researcher who went on to create Senketsu, the Scissor Blades and Nudist Beach. He was murdered by Nui Harime under orders from Ragyō.

His goal, as stated by Aikurō Mikisugi, was to "thwart the ambitions of the Kiryūins by using the Kamui," and his actions are the driving force behind the entire plot of Kill la Kill.

History
Sōichirō Kiryūin worked alongside his wife, Ragyō Kiryūin, in the research of Life Fibers, but turned against her after she disposed of Ryūko for her apparent incompatibility with having Fibers implanted into her body. Since he knew he would be punished for his betrayal, he taught Satsuki, at the time five years old, about the secrets behind Life Fibers, its research and her presumed dead sister, leaving her with the legacy of the rebellion against the Life Fibers.

Sōichirō faked his death after an assassination attempt by Takiji Kuroido. Presumed dead, he changed his appearance and took the new name of Isshin Matoi, taking Ryūko, who was thought to be dead, into his care. He then resumed his research on Life Fibers alongside Tsumugu Kinagase, Kinue Kinagase and Aikurō Mikisugi, and created the organization Nudist Beach. Over the years, he developed Senketsu and the Rending Scissors to counter the Life Fibers.

Six months before the events of the main story, Isshin was attacked by Nui Harime, who was sent to his laboratory to retrieve some important creation under Ragyō Kiryūin's orders. Knowing that, he hid Senketsu and lured Nui into stealing the Rending Scissors. He fought against her using them, but was eventually overwhelmed and mortally wounded by the scissors when Nui managed to snag them from his hands. In a moment of distraction upon hearing Ryūko's voice, who went to the house following a letter from Isshin asking her to have a conversation, Nui ended up having her left eye taken by Isshin, who broke the scissors in two halves. She took the scissor half used to damage her eye and fled. Ryūko found Isshin laying on the ground with the other scissor half driven through his body. He told her that, if she wanted to have a peaceful life, she was to leave him there and walk away. If she wished to fight in his place, however, she should take the very Scissor Blade that was used to wound him. According to him, she would be sure to find Isshin's assailant, but a cruel fate would be in store for her.

Before he could say anything else, Ryūko saw Nui wielding the Scissor Blade, but couldn't make out the silhouette. With the other half of the scissor in her hands, she immediately gave chase, ignoring the pleas of her father, who said he still had much to say. The mansion then exploded, Isshin still inside.

At some point before his death, Isshin sent a letter to Aikurō asking him to lead Ryūko to Senketsu.

Ryūko Matoi
According to Ryūko herself, they never had a close relationship. Isshin spent a great part of his time with his research, leaving him little time to spend with his daughter, which, added to the lack of a mother, led her to lead a lonely life and become a juvenile delinquent. However, while little is known about Isshin's actual personality, it is known that he obviously loved his daughter deeply, enough to risk his life by betraying his wife and her organization and sending a letter to Aikurō requesting him to aid her.

Satsuki Kiryūin
As her father, Sōichirō trusted her with the true nature of the Life Fibers prior to his disappearance and change of identity. Although Satsuki never knew it, Isshin Matoi was her father who disguised himself in order to raise Ryūko.

Ragyō Kiryūin
While Sōichirō obviously loved her at the time they got married, that love disappeared completely by the time Ragyō used her own daughters as test subjects to observe their resistance to Life Fibers. Sōichirō eventually left his wife and dedicated his life to counteracting her goals.