We often see duty and betrayal going hand in hand. If someone performs his duty, he's a person worthy of respect and admiration. But to not perform your duty is an act of betrayal, whether it's to country, family, or even yourself. But what if an act of betrayal is necessary to perform your duty? Now things are getting interesting, and it's this question The Left Hand of Darkness asks us to ponder. Estraven is considered a traitor by King Argaven, but is it possible that the only way to serve Argaven was to betray him? And how does that work anyway? We'll just have to read on to find out.
King Argaven performs his duty by sending Estraven into exile though he hates himself for doing so.
Ai's mission shifts at some point in the novel. Originally, his duty is to complete his mission for the Ekumen. By the end of the novel, his duty is to Gethen and Estraven specifically.