Who's reflecting who?

Today, while randomly hopping across the internet, I found an article that talked about how Dogs look like their Owners. Now, I've always believed this to be true because of that opening scene in 101 Dalmations where all of the dogs... look like their owners. I couldn't find a picture of it, but this one kind of does the job. 

The article says:

A group of 70 people who do not own dogs were asked to match photos of 41 dog owners to three possible breeds - Labrador, poodle or Staffordshire bull terrier. They matched the owners to the dogs more than half the time. Yet given three choices, they should have been right only about a third of the time. 

"This suggests that certain breeds of dogs are associated with particular kinds of people," said study leader Lance Workman, a psychologist at Bath Spa University in the UK.

So I read this and I started to wonder about the relation between certain dogs and certain people. Is it the person that looks like the dog, or is it the dog that looks like the person? Which one is the "Sun" and which one is the "Moon"? Is the person's appearance reflected by the dog, or do we reflect our dog's appearance. And is it on purpose? 

In class we talked about how, in the Traditional Gender Hierarchy, the Sun is a symbol for the dominant characteristic, where Truth and logic originates, usually belonging to the MAN. The Moon symbolizes the opposite: Madness rather than Logic, Rhetoric and Rope Tricks over Philosophy and Truth. The moon is an embellishment of the sun, or rather an attempt and failure to recreate it. It is a representation of the original, but it is not a presentation of it. It is a picture of an apple, rather than an actual apple. All art is then, a failed recreation of nature. If nature be Truth, Art is Rhetoric. And if Nature is secondary to God, then Art is false to the third power.

This is not to say that it is the actual truth--it is just a way of thought that dominated the gender roles of Elizabethan times, that was around long before, and still persists today. Shakespeare obviously understood that it was the norm, and he offered a validation of it, as well as a challenge to it. In Taming of the Shrew, he established that Man as the Sun and Woman as the Moon is the ideal norm. Kate was a failed attempt at a Woman trying to usurp Man's authority. It failed because Petrucchio used her own tricks against her. He used rhetoric and rope tricks to neuter her most devastating weapon, her language. During the most devastating example of Petrucchio's victory over Katherina--Act 4, Scene 5--Petrucchio has made Kate lie and say that the Sun is the Moon.

PETRUCHIO 

    I say it is the moon. 

KATHARINA 

    I know it is the moon. 

PETRUCHIO 

    Nay, then you lie: it is the blessed sun. 

KATHARINA 

    Then, God be bless'd, it is the blessed sun: 
    But sun it is not, when you say it is not; 
    And the moon changes even as your mind. 
    What you will have it named, even that it is; 
    And so it shall be so for Katharina. 

Even though the man is supposed to represent Logic and Truth, Petrucchio demonstrates the he is as mad or madder than Katherina. She even tells him "The moon changes as your mind", suggesting that he is a lunatic. Shakespeare is showing a clear example of Madness belonging to the male, but it is likely that Petrucchio is only using madness as a tool. Does this suggest that Petrucchio is reflecting Kate's so-called madness? And that he is acting like a Moon, making Kate the Sun? 

Who exactly is being reflected here? Kate or Petrucchio? And who has true authority? Does the Dog look like the Human? Or does the Human look like the Dog? Oh. My. God.

Eventually Kate has become the very definition of the Moon, reflecting Petrucchio's language even though it defies God and Nature "But Sun it is not, when you say it is not". Katherina now accepts the authority of Man and Petruchio. But I believe that although Shakespeare perpetuates the Traditional Gender Hierarchy, he doesn't really support it. I think this is so because he shows cracks at the foundation. Just as Kate has become the ideal love object, two more shrews appear in her absence: Bianca and the Widow, disobeying the orders of their respective husbands.

Is Shakespeare saying that it is an unwinnable battle between the sexes? It is definitely a lose-lose situation for one side, at least, according to the tradition. A woman who wants equality is labeled a shrew and is seen as a threat to male authority. A woman who wants to be loved is thus forced to surrender her rights to the man. Perhaps Shakespeare is pointing out the flaws in this foundation, and although he is definitely not condemning it, he's not saying it's perfect. In the pursuit of love, Men have to lie, and Women have to lie down and take it.