Why does Othello believe Iago over Desdemona?
In addition to Iago's "proof" of Desdemona's infidelity, there is the pervasive notion that no one in the play perceives Othello entirely as an equal. At the beginning of the play, when Iago and Roderigo are informing Desdemona's father, Brabantio, about the elopement of Desdemona and Othello, they euphemisms they use are completely dehumanizing. It is obvious that Iago and Roderigo believe Othello to be somewhat "sub-human." This is mirrored by Brabatio's horror at the marriage. Brabantio has had Othello at his house as a guest many times. Othello is acceptable to Brabantio as a houseguest but certainly not as a son-in-law. This lack of complete acceptance has shaped Othello's character. It is obvious that he expects to be rejected. He is too ready to believe the worst of Desdemona without her word.
Othello believes Iago over Desdemona because of Iago's "proof," such as Cassio leaving Desdamona very quickly and then right after Desdemona's pleading on his behalf. The hankerchief that Iago plants with Cassio, that once belonged to Desdemona, only cements Othello's trust in Iago. ALl of this "proof" of course is of Iago's creation, none of it is actually true. It is for these reasons that Othello believes Iago rather than Desdemona
I disagree with the above answer, i think that Iago is very much aware of the attitudes towards Othello, and that he plays on these to trigger emotions in roderigo.
He is constantly changing his moral values according to whoever he is attempting to influence and this is such an example.
As to why Othello beleives Iago, he plays on his temprement in order to rile him into frenzy. Othello does not think in the same way as the Venetian characters, possibly due to his ubringing.
The word of women was not particularly valued at the time either, this is evident in many of Shakespeare's plays, for example Much Ado About Nothing, when Hero's wedding is ruined.