Sōichirō Kiryūin

Sōichirō Kiryūin (鬼龍院 総一郎), also known by his alias 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 Ragyō's orders, impaled by his own Scissor Blade.

Sōichirō had aimed to "thwart the ambitions of the Kiryūins by using the Kamui". His actions are the posthumous driving forces behind the plot of the series—including Ryūko's search for her father's killer.

History
Sōichirō Kiryūin worked alongside his wife, Ragyō, in the research of Life Fibers, but turned against her after she disposed of Ryūko for her apparent incompatibility with them. Since he knew he would be punished for his betrayal, he taught Satsuki, who, at the time was 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 went into hiding after an assassination attempt by Takiji Kuroido; he changed his appearance and took the name Isshin Matoi, as well as Ryūko, who was also 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 anti-Revocs 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 a Scissor Blade from him. 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, Nui ended up having her left eye taken by Isshin, who split the scissors in two. 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 kill 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, the two 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. Coupled with the lack of a mother, this led Ryūko to lead a lonely life, eventually becoming 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 Ragyō and REVOCS, and sending a letter to Aikurō requesting him to aid Ryūko.

Satsuki Kiryūin
As her father, Sōichirō trusted her with the true nature of the Life Fibers prior to his disappearance and subsequent faked death. Although Satsuki never knew it until late in the series, her father had disguised himself as Isshin Matoi 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.

Senketsu
As Senketsu's creator, Sōichirō - as Isshin Matoi - left in the Kamui a bit of himself behind for Ryuko. Senketsu, in his normal state, shares the eyepatch and the "mustache" (part of the scarf) with Dr. Matoi's appearance. Senketsu only knows what his creator looked like. However, after Ragyō's defeat in Episode 24, he tells Ryūko that he is sure that her father is satisfied.