"Let him do his spite:
My services which I have done the signiory
Shall out-tongue his complaints."
This is Othello's instant response to Iago's concern (which, of course, is all a lie) about his and Desdemona's marriage. Othello believes that Desdemona's father, Brabantio, can do nothing to him or to his marriage because he is convinced that his reputation as a general and all the great acts he has performed for the Venetian military will outweigh any slanderous accusation that Brabantio can throw at him.
His self-confidence turns out to be justified since the Duke of Venice concludes that there was nothing wrong in Othello's actions and that he did not, as Brabantio swore, use magic or potions to ensnare Desdemona. However, this intense belief in his own righteousness turns out to be, quite literally, Othello's fatal flaw throughout the course of this play.
Right here, at the beginning of the story, we see evidence of Othello's own powerful bias towards himself. A few lines after his assertion that his deeds as a general will have great standing with the Duke, he tells Iago that he truly loves Desdemona and says,
"I would not my unhoused free condition
Put into circumscription and confine
For the sea's worth."
He states that he would not give up his freedom for anything less than absolute love. These several lines are telling, because like every best man in every modern movie about a wedding, he seems to consider marriage to be a great burden, or at least a confining existence. This subtly sets up the idea that Othello doesn't properly appreciate Desdemona and their love.
Othello's self-righteousness and failure to believe that others can be as great and righteous as he ends up being his downfall. Iago's deceptions only work so well because Othello has no faith in others, particularly in the loyalty of his wife. He declares boldly throughout the play that he loves Desdemona greatly, and even though she chooses him over her own father, he refuses to believe in her fidelity at the end. Ultimately, his inability to trust his wife results in him murdering her and subsequently killing himself.