Byakko was once one of Abe no Seimei's powerful Shikigami. Later he and other eleven Shikigami entrusted themselves to her twelve companions, and the twelve Shikigami continue to provide power to chosen decendants of the companions.
As Byakko himself, his standard of choice is, the new host should be strong as well as caring and protective to others. This was the reason that he skipped Togen Amawaka after his father Kogen, to Togen's son Seigen instead - Togen was distorted and absorbed in executing people for honour.
He once ridiculed Seigen eager to finish and see his love interest in battle.
Before the fight with Hijirimaru and Higano, Seigen gave the Reifu to his daughter Mayura and let her to aid Shimon, Benio and Rokuro. While Higano tortured Mayura and asked why an exorcist so weak like her would be in Magano, she cried out that, what she wanted is to help harmed people in front of her.
Byakko then emerged from Reifu to Mayura's mental world and noted that she was just like Seigen. Ironically, Mayura mistaken him as a impurity or a monster at first glance. He told Mayura that he the Shikigami Byakko of Twelve Guardians, and asked her whether she want his power and stick to her ideal of protecting people. Mayura confirmed and gain the power of Twelve Guardians.
After Mayura arrived at Tsuchimikado Island, Mayura felt herself still not utilized the power of the Twelve Guardians, and wondered that if she was truly accepted by Byakko. He emerged and denied that, and stated that once an exorcist has the Twelve Guardians' power, she/he would be fully accepted by the Shikigami. Later Mayura used the water mirror to communicate with him several times.