Because he took his wife family name and became part of her family... in some countries you belong to the family you marry and many times is the most powerful family the one you become part... in other words, he doesn't belong to his original family once he married but to his wife family!!!
Because also many cultures men are seen as head of the family and not women, many times a family that only have a daughter marry her to a man to become the head of the family, because a marriage is like an adoption, he became part of the most powerful family and will become the head of the family, so he is still seen as the son of the family after losing his wife!!!
And now, when he marry again his new wife will also belong to the most powerful family including her children, that is why children whose parent who took custody marry again also change their last name...
The oldest brother is most likely the true leader of the family-since he was of age when his mother passed away, and was acknowledged as the heir- but in the immediate family, the father is deferred to, as being head of the family.
After rereading it, I'm finding a lot of inconsistencies. For one, Souya's mother's marriage into the family. Souya mentioned that Kazuki's father married into his mother's family and had to fight tooth and nail to stay. But that his kother wasn't a good person????
So, if Kazuki's father married into the family, then if the mother isn't in the picture anymore, how is he still the head of the family? How did Souya's mother marry into the family when her husband isn't blood related to the family?
Secondly, how far apart in age is Kazuki and his real brother????? They're making it seem like the two are 20 years apart in age or something.