seems to me like noam swerved the lady's second question of "what is legitimate authority?". i mean yeah its on the authority to provide an answer, but its also on the accuser to have a standard to which to judge that answer.
for instance, taking his "grabbing the child" example, he provided an argument to show the legitimacy of his actions, but what if someone else simply disagrees with not just reasoning but his core premise of grabbing the child? at that point the parties are at a standstill. what then?