In Act II, scene iii, Othello strips Cassio of his rank because he:
1.) has been drinking excessively while one duty.
2.) gets into a fight with Roderigo.
3.) injures Montano, governor of the island.
4.) disrupts what should have been Othello and Desdemona's honeymoon night together.
5.) is a younger, white, better-looking man than Othello, and Othello may have been already jealous of him, thereby setting him up to fail by placing too high of rank and expectations on him to begin with.
Iago orchestrates Cassio being stripped of his rank. He is jealous that Cassio was promoted ahead of him and wants to bring him down and take his place. To do so, he persuades Roderigo to pick a fight with Cassio, convincing Roderigo that if he can get Cassio out of the way, Desdemona will fall for him once she tires of Othello.
Iago know that Cassio is "rash" and hot tempered, and he tells Roderigo to try to get Cassio to strike at him. Iago then says he'll "abuse him [Cassio] to the Moor" because, as well as hating Cassio, he "fears" him and wants him out of the way.
Iago's plan works. Iago gets Cassio to drink too much, Roderigo provokes Cassio so that Cassio strikes him, and when Montano, the governor of Cypress, intervenes, Cassio wounds him. Iago, under the guise of wanting to "help" Cassio, has already falsely advised Montano that Cassio has a drinking problem, so Cassio's behavior simply confirms to Montano that he is an alcoholic.
We see Iago's duplicitous nature at work again when Othello asks him about the fight. Iago says: "I should rather have my tongue cut from my mouth/Than it should do offence to Michael Cassio," before "unwillingly" offering a version of events that leads Othello to cast off Cassio.