In Othello, there are 3 women and 3 men, and here's how they match up: Othello - Desdemona (upper-class); Iago - Emilia (middle-class); Cassio - Bianca (low-class).
The two main women, Desdemona and Emilia, change substantially during the play. They are foils of each other: Desdemona is idealistic and traditional, whereas Emilia is realistic and jaded. Both of them are deceived and murdered by their husbands. Shakespeare seems to be saying that his society was more sexist than racist. They are the victims of male revenge and jealousy.
Desdemona goes from being very vocal in court and defiant of her father in Act I. She secretly elopes with a black man, which would have been scandalous. Not only that, but she talks the Duke into letting her accompany her husband to war. After Act II, she is as submissive and quiet as a mouse. She knows she's going to die, and she does not fight or call for help. In all, she seems like two different characters: a vixen in Act I, and a passive victim in Acts II-V.
Emilia changes the other way. She goes from being chatty in Act II to openly defiant of her husband in Act V. Iago is a misogynist who openly slanders women in Act II ("You rise to play and go to bed to work”), yet she says nothing. Only after Desdmona is murdered does she cry foul. But, she is the hero of the play, the only one with enough courage to call men what they really are ("[men] are all but stomachs, and we all but food; They eat us hungrily, and when they are full, they belch us.")
Overall, Othello goes from treating his new bride as a goddess to a whore, all because of an accusation. This suggests that women are set up to fail, that they are victims of impossible standards (even double-standards), that they are play-things, status symbols, toys, and food for men.
As such, women are afforded no voices. They cannot defend themselves, and no male stands up for them. An outspoken woman was the same as an unfaithful one, such was the misogyny inherent in the macho culture. Desdemona's fallen status as a whore even below Bianca suggests that men may not have loved women at all, only used them for work and play.