Tradition
Hiashi hated tradition.
It was tradition what determined that he had to marry a weak women whose body was found floating on Nakano's river waters the morning after her lover was proclaimed killed in action.
It was tradition what took his brother from him so early in his life, when he didn't even could grasp why someone so similar to him had such a different destiny. And was also tradition the reason why he couldn't protect his little brother in the end.
Free men could choose to be shinobi or civilian, Hiashi could not. Tradition dictated that he not even had to be a shinobi but the best of his clan, but also thanks to tradition none of his talent could be used to protect his village because he was the firstborn of Hyuuga Hiroaki and was meant to be the next leader.
All of this meddling with his life, his loveless marriage, the resentment of his brother made Hyuuga Hiashi despise tradition, and this feeling grew even stronger when his wife bore a daughter for the first time.
A daughter was not what traditionally was expected from him. Especially when his younger brother was able to bring a son to the world in the previous year. A son who each day grew stronger, a son born from a bloodline as pure as his daughter but different from Hinata, a son brought by love.
But it was only after a decade since his first child was born that he decided to do something to stop tradition's trail of disgraces. He would not let it destroy his child's life as it had made with his and his brother's. The child was weak, and he didn't see any other way to save her. He then challenged tradition, going against his own father and the whole council, he broke the curse mark from Hizashi's son in exchange for his oath that he would protect his weak daughter, and lead the Clan, starting a new era in which tradition wouldn't encage the Hyuuga's destiny anymore.