Question: why did byakuya betray the soul society?
Answer: Senbonzakura explains why Byakuya faked his betrayal. When Senbonzakura states it was all for the purpose of learning where Kōga had been sealed away, Ichigo and Rukia express surprise as Senbonzakura says destroying Muramasa alone would be meaningless and proclaims the one who had to be defeated was Kōga.