Answer: Whether Iago's desire for revenge is justified depends on how we approach this issue. If we take into consideration his racial prejudices, his desire for revenge is not justified.
Step-by-step explanation:
Iago has multiple reasons to hate Othello and Cassio and seek revenge.
The first one is that Othello passed him over for a promotion and chose Cassio for his lieutenant. Cassio is his rivalry, which explains why Iago is going after him, too.
The second reason, that becomes evident in Act I, scene III, is that Iago suspects that Othello engaged himself in an affair with Iago's wife, Emilia.
Iago's third reason, stronger than the two previous excuses, is a pure racism. He calls Othello ''a Barbary horse'', ''the Moor'', ''old black ram'', and directly expresses racial intolerance. Iago's desire for revenge has its roots in his belief that Othello, given his race, is not worthy enough to be a top-ranking officer. In this light, Iago's desire for revenge is not justified, as he has racial prejudices.