WARNING: The following contains spoilers for Ayashimon Chapter 13, "I Refuse to Lose Again" by Yuji Kaku, Adrienne Beck, and Brandon Bovia, available in English via Viz Media.
The driving force behind Ayashimon's Urara is wanting revenge for the death of her father, former head of the Enma Syndicate Kioh. This was revealed back in Chapter 2, but the circumstances surrounding his death have remained shadowed in mystery. In Chapter 13, Ten says that the cause of death was never announced, and the Onmyo Bureau only said that Kioh was dead and the different factions that control Kabukicho splintered off and began fighting each other despite seemingly being close to the former chairman. So what happened to cause the rift and how did Chairman Kioh actually die?
While there's not a lot of information to go on, it's entirely possible that Chairman Kioh was killed in a Ritual Duel. Kotton's reaction to potentially losing custody of Urara hints at something traumatic and dubious happening to Kioh in front of him. At the beginning of Chapter 13, he says "This time...This time for real I won't...!" This is obviously him having regret for not stepping in during Kioh's death, and in the previous chapter, he admits to being there the day he died. "Boss Kioh really was like a father to me. And yet...I was there...But he still..."
With the information given about Ayashimon culture and the silence about the cause of death, it's obvious there's some sort of coverup. This means that Kioh's death wasn't natural and that someone has connections and influence to keep everything hush-hush. The only person introduced so far with connections in the Onmyo Bureau and the police is Akari Doppo, the new chairman of the Syndicate. He's been shown colluding with one of the Onmyo agents and using them to gather information about Maruo and Urara, so covering up Kioh's death would be simple for him as long as he had something worth trading for. It's possible that he challenged Kioh to a Ritual Duel in a bid to take over and Kioh was killed as a result.
Doppo has been shown to not bat an eye when it comes to killing someone, especially when they get in his way, but there's not a lot of information on what his relationship with Kioh was like. Kotton viewed Kioh as a father, and Urara clearly loved him despite never being able to be with him. Being made Second-in-Command takes a great amount of trust, especially in a group like the Yakuza. Either Doppo was playing a long-con and pretending to respect Kioh and then challenging him or something happened that made him completely lose faith in Kioh and want to take over. With how Kioh wanted to keep Urara secret and protected, it's possible he knew that he would be betrayed and would die. Doppo has his "collection," which Kioh would most likely have known about. He had to have known about or at least suspect Doppo's true nature.
There's also a small possibility that Kioh faked his death, but that seems unlikely as Kotton was an eye-witness and seems so heartbroken. That doesn't totally rule out this possibility, and it's still early in the story. The only way to find out the truth is to speak to all of the people who were close to Urara's father and that were there on the day of his death.
