why does cole throw away the hair he pulled from the spirit bear

People didn't believe that Cole had encountered his Spirit Bear. Cole finds himself once again defending his word and integrity except this time he doesn't have an angle; he isn't playing games. At the end of the chapter Cole reaches into his pocket and feels the Bear's fur he had ripped out. He throws it into the water because from now on, "His words would become his only proof." I'm not sure I would have had the guts to do what Cole did. I'm afraid I would have displayed the fur to prove my side of the story.