Why does Othello hate Cassio?

Othello begins the play liking and respecting Cassio. He promotes him to lieutenant, a position Iago believes he deserves. Iago, on the other hand, hates and resents both Othello and Cassio (Iago despises everyone). Iago plots their mutual destruction by manipulating Othello so that he becomes jealous of Cassio. Iago, in this way, kills two birds (Othello and Cassio) with one stone.
Othello only begins to doubt Cassio after Iago fans the flames of his jealousy. Iago knows Othello is insecure about Desdemona's love. He causes Othello to believe that Cassio and Desdemona are having an affair and persuades Roderigo to stab Cassio. Iago knows that once Cassio is dead, he can't set Othello straight. Iago would also simply like to see Cassio dead.
Iago's plot works. Othello does turn against Cassio in that he does believe he seduced Desdemona.

In the play, Othello doesn't really hate Cassio until Iago manipulates him into doing so. Essentially, Iago is the one who plants in Othello's mind the idea of Cassio having an affair with Desdemona. Of course, Cassio is innocent, but Othello's jealousy prevents him from thinking clearly.
The play actually begins with Iago complaining to Roderigo about Cassio's promotion to lieutenant. Iago has nothing but contempt for Cassio because he thinks that the latter is an effeminate "arithmetician." He maintains that Cassio knows less about battle than an old spinster.
In Act 2 Scene 1, Iago's jealousy flares up when Cassio kisses Emilia (Iago's wife) in greeting. One can conclude that Cassio is a natural flirt who enjoys the company of beautiful women. He lavishes praise on them and delights in making them smile. However, Cassio's easy ways with women arouses Iago's hatred and jealousy. Using subterfuge and outright fabrications, Iago is able to inspire in Othello the same negative emotions about Cassio that he has. So Othello hates Cassio because he suspects that his lieutenant is bedding Desdemona. However, one can argue that Othello may never have come to despise Cassio if it wasn't for Iago.