In Book VI of Homer's Iliad, why does Hector rebuke Paris?
In Book VI, Hector rebukes Paris because of his younger brother's selfishness.
Hector enters Paris's home, described by the poet Homer as "fine" and "built by the best workmen in the fertile land of Troy, in Book VI with a sense of disgust in his heart. This disgust communicates how Hector feels about the state of affairs in which Troy is immersed. On one hand, Hector fights for Troy, but he also cannot accept the reasons Troy is involved in conflict because he knows so many will die for so little.
Paris does not fight on the battlefield. The emotional tension caused by this is evident in Hector's rebuke of Paris when he enters the home and sees Paris practicing with his weapons. Paris's failure to fight is the basis of hector's fury as he calls Paris "perverse," and the contradiction between Paris's public and private actions is the basis of his disgust:
It is wrong to be so perverse, nursing anger in your heart, while your friends die at the gates of the city and high on the battlements, yet you are the reason the sounds of war echo through Troy. You yourself would reproach those you found shirking the field of battle, so rouse yourself, before flames consume the city!
Hector sees "shirking the field of battle" as one of the worst crimes imaginable. He sees it as cowardice. Hector recognizes that "friends die at the gates of the city and high on the battlements" because of Paris's affections for Helen and failure to act. Because of the King's wishes, Hector must stand by his brother, but that does not mean he approves of his actions. Hector's furious rebuke is a way to chastise his brother and spur him toward more manly action. It is also a way to force Paris to be accountable for his actions.