Iago gives more than one reason to hate Othello, and the first is the lieutenancy: in Act I, Scene 1, he tells Roderigo that three nobles of the city went to ask that Othello name him, and Othello chose Cassio. Because of this, he says, he will be "only the ensign of Your Moorship!".
The second is a suspicion. In Act I, Scene 3, alone, Iago says: "I hate the Moor", and that it is rumored Othello "has done my office", that is, that he has lain with Emilia, Iago's wife. He admits he does not know whether it is true, but acts as if it were. In Act II, Scene 1, he repeats the suspicion ("He has mounted my saddle"), says he loves Desdemona "for the mere diet of revenge", and adds that perhaps Cassio also "has slept in my nightcap".
There is also a motive tied to Cassio. In Act V, Scene 1, Iago calculates, in an aside, that if Cassio lives, "He has a constant beauty in his life", which makes Iago look uglier, and that the Moor can expose him before Cassio. For this reason, he concludes, Cassio must die.
Iago also acknowledges qualities in Othello, whom he describes as "of a constant, amiable and noble nature", and it is from the open character of this man that he draws his plan: in Act I, Scene 3, he says that Othello "thinks honest the one who only seems to be" and that, for this reason, he can be led "by the nose". At the end of his list of motives in Act II, he admits: "It is all here, still confused." Iago gives more than one motive and does not choose one.