Because he's a coward. He feels that what the Association is doing is wrong, but he dares not actively oppose them because he doesn't want to jeopardize his wealth and social status. When James asks him what will he do, Billy responds "I'm a victim of our class, James."
Billy becomes an ineffective, self-loathing drunk, a man of words and not of deeds. He goes along with the Association but is reluctant to get his hands bloodied in the fighting. He tries to remain a bystander, but in the end the violence affects him too.