Part I:
"Sinat Achim" & Idealism
To uncover the motive behind the brothers' hatred of Yosef, we must return to the story of Yosef's dreams (at the beginning of Parshat Vayeshev). Let's begin with a quick review of these two dreams:

1. "And behold we were gathering sheaves in the field, and my sheaf stood up and remained upright; then your sheaves gathered around and bowed down to my sheaf." (37:7)
2. "And behold - the sun, the moon, and eleven stars were bowing down to me." (37:9)

One need not be a prophet in order to interpret Yosef's two dreams. Clearly, they point to his developing sense of superiority over the entire family. However, they also echo an earlier sibling rivalry in Chumash - that between Yaakov and Eisav! Recall the blessing that Yitzchak gave to Yaakov, though he intended to give it to Eisav:

"May God bless you with ... an abundance of grain ... Be master over your brothers, and let your mother's sons bow down to you." (27:28-29)

This parallel suggests that Yosef's dreams may not only hint to his future leadership position, but they could also point to Yosef as the only 'chosen son,' just as Yaakov himself emerged as Yitzchak's only chosen son! Add to this:

Yaakov's love and special treatment of Yosef (see 37:3);
His "ktonet pasim" (special cloak), a sign of royalty;
Yosef is the first son of Rachel, Yaakov's 'primary' wife;
Yaakov's silence regarding Yosef's dreams (see 37:11);

This background allows us to suggest an ideological basis for the brothers' decision to kill Yosef.