The clan leader's oath is not impossible, just extremely rare; typically, it is taken before someone becomes a leader. Also, if the descendants of the leader are outstanding enough, the tribe's wizards will try to avoid having them take the oath.
By the way, if the other party in the oath dies, the oath becomes void.
"I will inform the tribespeople..." Chun Xi said after contemplating for a moment; she still couldn't abandon Du Gang's descendants, and nor was she ready to give up her position as clan leader.
Therefore, she didn't plan to engage in the challenges Du Gang mentioned; after all, Du Gang was an outsider, and outsiders eventually leave. Even if Du Gang defeated her, could he stay here forever?
Staying forever here is not an issue, but would he?