The hierarchical laws of Athens surely support a patriarchal order in which a father may have his daughter severely punished for marrying against his wishes. Shakespeare undercuts this hierarchical patriarchal order in A Midsummer Night's Dream by rendering Athenian law subject to the influence of the moon and fairies.
In contrast to Athens, the woods is where fairies gather, lovers conspire, actors rehearse, spells are cast, manipulations backfire and reconciliations begin. Shakespeare uses the anarchy and the associated fairy monarchy of the woods to illustrate a new proposition for the balance of power between anarchy and hierarchy.
Hierarchy is defined by Random House Dictionary at Dictionary.com as any system of persons or things ranked one above another, and patriarchy is defined by the same source as the male head of a family or tribal line.
The town representative of hierarchy and traditional patriarchal governance is Theseus. Throughout A Midsummer Night Dream, the moon is equated with love and marriage. Theseus is waiting for his marriage that will take place according to the moon's governance at the phase of the New Moon. Furthermore, wedded fairies Oberon and Titania have flown in with their retinue from India to give their blessing to the government representative Theseus's wedding to Hyppolyta. While Theseus upholds order in Athens, he also undercuts the order by revealing the ruling influence of other powers that sway the realm of order.
In the woods, trickery, magic and anarchical schemes give the rule of order--or rather, the rule of anarchy--while people try to manipulate each other into what they want for their own (often selfish) reasons. Shakespeare reveals in this that anarchy and hierarchy share the feature of manipulation of others' lives in common with each other. Shakespeare uses this and Theseus's wedding to suggest a true balance between the the rule of order and the rule of the more mysterious forces of the world to achieve a state where individuals are honored and respected instead of manipulated.
This statement makes a lot of sense. Just look at how things are in this play.
When we are in Athens, we see Egeus being able to completely control Hermia's life, at least legally. Theseus and Egeus are men who get to dominate the lives of women. Therefore, it is a hierarchical, patriarchal order.
Out in the forest, in the meantime, there is no such order. Although he is king, Oberon cannot order Titania to give him the changeling -- this shows a lack of patriarchy and hierarchy. Disorder can be seen in all the shenanigans that happen with Puck and the love potion.