In defense of Iago in Othello, why does Iago do what he does? What are his motives?

There may not be a justifiable defense of Iago's actions. Iago creates havoc mainly to create havoc. There is not valid reason. Iago is purely evil and likes to toss evil like a hand grenade in the lives of people around him.

Iago's stated reasons are based on rumor or supposed slight. There is not sold foundation to these that would give creedance to the need to seek revenge. First of all is the rumor of his wife Emelia's infidelity with Othello, something that has no merit beyond idle gossip about an outsider (Othello). Yet Iago is angered, not so much by the intended slight to his wife's honor, but to his own. By being the subject of such a rumor (and being cheated on by one's wife usually brought blame upon the husband for being "insufficient"), it is Iago's reputation that is damage. Iago would rather his wife be secretly unfaithful than for her to be falsely accused publicly.

In reference to Othello, Iago is upset that he has been passed over for promotion by someone whom he considers to be a lesser man. He believes that his experience alone should make him more worthy than Cassio to be Othello's lieutenant. Though not stated explicitly, it is possible that Othello sense in Iago some character flaws that would not make him a good leader of men (as indeed there are).  To Iago, character is less important that one's actions, whether or not they are nobly performed. To Iago, these two public slights are justification enough to ruined the lives of as many people as possible.

Throughout the play, Iago's over-confidence prevents him from seeing even the possibility that he may be discovered. It is only when he is exposed at last by Emelia that he realizes that his reputation is completely gone, and so he kills Emelia himself, having effectively destroyed the lives of Othello and Roderigo.

To the end he refuses to speak, to even justify himself in his own defense.