why did Iago want to destroy othello?

Iago is jealous of Othello, but even more than that, he wants to punish Othello for promoting Cassio to lieutenant. Iago expected the promotion and took his anger out on the man he believed slighted him.

Iago has suspicions that Othello (and Cassio, who Othello promoted) slept with his wife.

This, however, is not confirmed and Iago acts out of anger towards both Othello and Cassio; seemingly believing his worth is more than that of the two he tries to sabotage.

This lack of a stable motive makes the character of Iago especially sinister - often referred to as a villainous individual due to this ‘motiveless malignity’

Othello is described as a "black ram", Iago is subconsciously racist which is a part of the reason why Iago dislikes Othello. Iago also resents Othello because he wanted the position of lieutenant.

Iago seeks to destroy othello because of two main reason.

The first reason was that, Iago suspected that, Othello had slept with his wife, Emilia. He tries everything possible to ruin othellos marriage as a for of revenge or payback for Othello though he does not have any concrete evidence of this crime.

Secondly, which could be seen as the main reason behind his plot for Othellos downfall was the refusal of othello to give him the place of the lieutenant. It can be seen vividly in the drama that Iago was strenuously seeking for the place of the lieutenant as he writes letters to great people of the city for them to persuade Othello to appoint Iago as a lieutenant. Othello rather brushes away all Iagos efforts and tells him that he has already chosen his lieutenant which was Cassio. Iago believed that Cassio did not deserve such a position because all he knew was bookish theories about war and that Cassio has never set foot on a battle field. This enviness for Cassio and hate for Othellos decision makes Iago plot on how to destroy Othello.