We are all driven by something. Revenge. Hope. Love. Hate. Illidan was no different. Resentment and bitterness churned in his heart, fueling his every thought and action.
The resentment came because he felt inferior to Malfurion, whose deeds always overshadowed Illidan's own. One example of this occurred when the Stormrage brothers both studied druidism. Illidan had already learned sorcery, but he desired to master the druidic arts as well. Such was not to be his fate, however. Whereas Malfurion excelled at wielding nature magic, Illidan failed.
The bitterness stemmed from Illidan's love for Tyrande Whisperwind. He adored the priestess, but she did not reciprocate his feelings. I think he also feared that Malfurion would inevitably win her heart.
Over time, he became obsessed with destroying the Legion, and he criticized any ally whom he saw as incompetent. He directed most of his ire at Latosius, the elderly commander of the Moon Guard sorcerers. To Illidan, Latosius symbolized everything that was wrong with the resistance. The old elf was stubborn, unimaginative, and timid. His ineffective tactics wasted the sorcerers' talents. More that once, Illidan claimed that he could do a better job at leading the Moon Guard.
When Latosius fell in battle to the Legion, Illidan would have a chance to make good on that claim.