The primary belief in the play regarding the sexes is that there are conventional roles for men and women in society.
A woman's honor is based on her chastity, while a man's honor is based on his friendships with other men. Women have no recourse if their honor is questioned, as is the case with Hero, while men can challenge another man to a duel if his honor is denigrated.
The expectation in this play is that males and females have certain defined roles, certain behaviors are acceptable and if the rules that govern behavior are violated, there are serious consequences.
The play also examines the meaning of marriage, a social contract between two people, where love need not be the driving force for a union. When Claudio decides to woo Hero, he uses all the rules of proper courtship to express his feelings.
But when he believes that she has been unchaste prior to their marriage, he no longer wants to marry her, because she has violated her honor. She is therefore ineligible in Claudio's eyes and he does not hesitate to shame her in front of her father and others.
The fact that Claudio is willing to marry an unknown woman, is further evidence for the idea that marriage is not about love.
The other relationship is between Beatrice and Benedick. They have an adversarial relationship, always fighting. They relate as two equals, unlike Hero and Claudio.