During Shakespeare's time, there were clear societal rules that women were expected to follow. These cultural expectations greatly influenced how Shakespeare presented many of the women in his plays, including the women in A Midsummer Night's Dream.
Although England was ruled by a strong female monarch for much of Shakespeare's life, women in general were considered the inferior sex. They were thought to be weaker, both physically and mentally. As such, they were believed to require a man to take care of them. The role of the caretaker was usually fulfilled first by a woman's father and later by her husband. In many ways, women were commodified. They were seen as objects that men controlled and could even trade between each other. Egeus makes this position clear when he says of his daughter Hermia, "she is mine, I may dispose of her" (1.1.42).
Hermia would like nothing more than to wed Lysander. However, her father has arranged for her to marry Demetrius. In the play, the law requires Hermia to acquiesce to her father's wishes or face death (although Theseus offers a third option of becoming a nun). Although the laws of Shakespeare's England were not quite as harsh as those in the setting of the play, the original audience would have been familiar with the concept of men being in charge of female family members.
Shakespeare's culture also dictated that it was not a woman's place to make romantic overtures. Helena points this out when she tells the audience, "We cannot fight for love, as men may do / we should be wooed, and were not made to woo" (2.1.226–227). In this context, we can see that any instance of women wooing men in this play was meant to be comedic in its absurdity.
There is a moment in act 2, scene 1 where Helena begs Demetrius to take a romantic interest in her. However, her argument indicates that women of Shakespeare's time could expect to be ill-treated by their husbands while remaining subservient. Helena tells her love interest,
I am your spaniel. And, Demetrius,
The more you beat me, I will fawn on you.
Use me but as your spaniel—spurn me, strike me,
Neglect me, lose me. Only give me leave,
Unworthy as I am, to follow you.
What worser place can I beg in your love—
And yet a place of high respect with me—
Than to be used as you use your dog? (2.1.188–195)
None of this is to say that women were always blindly subservient to men. Throughout the play, Shakespeare shows women exercising a degree of opposition to the patriarchy in several subversive ways. For instance, Hermia runs away instead of following her father's wishes. She even speaks her mind to Theseus when he tries to convince her to marry Demetrius.