Hermia refuses to marry Demetrius (I i 59-82), because she loves Lysander. Her father, backed by the laws of Athens, threatens her with death or a nunnery if she doesn't marry the man he has chosen for her. Andrew Gurr points out that several of Shakespeare's heroines rebel against marriages that are arranged by parents:
Shakespeare's presentation of marriage was relatively "new", in that his plays uphold the power of love over parental authority. Juliet's rebellion against the Capulets' insistence that she marry the man of her parents' choice was an act of disloyalty which few London citizens were ready to applaud. Shakespeare's heroines were an alarming novelty. When Beatrice challenged the convention of women undergoing arranged marriages (Much Ado, II.i.42-7) and the young lovers in A Midsummer Night's Dream rebelled against the harsh Athenian laws they were voicing kinship with Juliet. (Gurr 1987:149)
In A Midsummer Night's Dream, love and parental authority seem to come to a compromise. But although the women have a say in choosing their husbands, the institution of marriage is as determinedly patriarchal as ever.