While he was running, Billy had some time alone to think about why he decided to leave the party aside from his anger. The fact that his friends were a bit naive and wanted to help everyone was probably the main reason while Billy would be fine in just helping the people close to him when they needed him. Even if they come to an agreement to reach a middle ground the next time, even if they follow his lead, they wouldn't like it, and thus that would lead to bigger problems down the line.