How does Benedick and Beatrice's behaviour challenge gender roles?
Does the answer change according to whether we are thinking about Shakespeare's time or our own? Possibly thinking about Act 4 Scene 1 in particular.
In regards to Beatrice particularly, consider these examples:
She quickly rejects Don Pedro's proposal, without consulting the "advice" of her father. She is in contrast to Hero, who listens carefully and receives instructions from her father as to how to handle the proposal from Don Pedro/Claudio.
She advises Hero to do "as it pleases [herself]". She is encouraging her cousin to act according to her own desires and not to be subject to the wishes of her father.
She immediately seeks a violent reaction to Claudio's slander of hero. She wishes desperately to be able to challenge Claudio herself, but understands her limitations, and asks Benedick to do it for her.
She is, like many of Shakespeare's heriones, not at all the typical Elizabethan woman.
Beatrice's behaviour challenges gender roles, particularly for a Jacobean audience, from the very start of the play. Her outspokenness and witty banter with the messenger in 1.1 is contrasted with Hero's quiet submissiveness in this male world. At the start of 2.1, Leonato warns Beatrice that she will not get herself a husband if she 'is so shrewish [of her] tongue.'
Benedick challenges gender roles must less obviously in the first half of the play. He sees himself as attractive to women, but is resolutely a bachelor, a soldier and a 'lad'. He changes, though, as he's tricked into discovering his love for Beatrice. In the failed wedding scene, 4.1, he and the Friar are alone among the men in not condemning Hero. Hero is subjected to a torrent of misogynistic abuse, by Claudio, Don Pedro and, horrifyingly, by her own father. Benedick builds on the friar's suggestion that there is 'some misprision in the princes', and looks to Don John as its author.
Later, alone with Beatrice, Benedick must confront the stark choice that she has presented him: if he loves her, he must 'kill Claudio'. She in turn has railed against gender roles, wishing herself a man, that she might 'eat his heart in the market-place.' Initially, Benedick is horrified, but on hearing Beatrice confirm that she thinks 'in her soul that Count Claudio has wronged Hero', he accepts the truth of her instinctive, unshakeable and feminine faith in Hero and goes to challenge him.