Answer:
Agamemnon was the King, who was born to rule, but he didn't have the capability to do so. While Achilles was the king, who had the ability to rule, but couldn't utilize it properly. Both had a bad temper and were always trying to portray themselves as the heroes for Greeks. Neither of them was ever willing to compromise, or accept a status lower that that of a hero. This was the main reason behind their dispute of Briseis, which resulted in the loss of hundreds of soldiers on both sides. They were never appropriate to be declared as heroes.
For early Greeks, courage and strength of a person, along with his honesty towards his people, contributed majorly towards that person's rank in people's eye. Hector at that time, was the commander of Trojan Army and was considered as the future King of Troy. No one had a match for his valor and bravery. Apart from that, his sense of responsibility and concern for Trojan women and the community also made him a hero in the eyes of his people.
