Final answer:
Iago hates Othello because he believes Othello has had an affair with his wife, Emilia.
Step-by-step explanation:
The character of Iago in Shakespeare's Othello harbors resentment towards Othello for a number of reasons. One prominent reason for his hatred is that Iago suspects Othello has had an affair with his (Iago's) wife, Emilia. This reason is highlighted when Iago speaks to himself, suggesting that he believes Othello has slept with his wife and stating, “I hate the Moor: And it is thought abroad, that 'twixt my sheets He has done my office.” This accusation forms part of Iago's motivation for the deceitful and destructive actions he takes throughout the play.