My guess: Yakyō is the elder brother by about 2-5 years. Their father wanted to sell the cafe, and Kyosui refused. They had a fight and the father told Kyosui he was on his own and wouldn't help him with the shop—Kyo swore he wouldn't come back even if he had to. Yakyō has tried to convince Kyosui to return to the family, but Kyo told him he wouldn't go back, Yakyō insulted the cafe, and now they're fighting too. That's usually how it goes for these stories LOL