http://revach.net/article.php?id=1977

Section: Moadim   Category: Megilas Esther
Mordechai vs. Haman - A Warrior Backed By Tradition

Why was Mordechai chosen to wage battle with Haman? Chazal say that since Haman was from Esav, he was to be brought down by the children of Rachel Imeinu, specifically Binyamin.

Binyamin was the only brother who didn't bow to Esav when Yaakov met his brother (he was the only brother not yet born). Because of this, Mordechai felt that he didn't have to bow either, just as his ancestor had refrained.

Some say that all the brothers involved in the sale of Yosef hurt their father and disrespected him; only Binyamin was not involved, while Esav was famous for his adherence to the one law of Kibbud Av Va'Eim. Even Yaakov ran away from home and lost 22 years of being able to adhere to that mitzvah. Since Binyamin was the only one to be worthy in this area, he was chosen to fight against Esav, and this included his descendants as well.