Katherine is at first shown as a woman who is at war with all of those around her. The first sign that there is something amiss is that Katherine appears before Petruchio in the play. She first appears in the first scene and he follows her in the second. She, then, precedes him in the order of creation, indicating that chaos is in the ascendant. The first lines then spoken by Katherine are an accusation that her father is trying to turn her into a prostitute, an exhibition of her contempt for the familial and social hierarchies of the Elizabethans: “I pray you, sir, is it your will / To make a stale of me among these mates?” She follows this up with a rejection of any desire for marriage coupled with insults and threats of violence against her younger sister’s suitors. Addressing Hortensio, she says,
I’faith, sir, you shall never need fear;
Iwis it is not halfway to her heart.
But if it were, doubt not her care should be
To comb your noodle with a three-legged stool,
And paint your face, and use you like a fool.
These are no idle threats as she is indeed depicted, as Coppélia Kahn has pointed out, committing “four acts of physical violence onstage,” three of which are against men and one against her sister. Katherine even follows up on this threat of violence to Hortensio in particular when she smashes his head with a lute while he attempts to give her music lessons. As Hortensio, disguised as “Litio,” a music teacher, tells it,
I did but tell her she mistook her frets,
And bowed her hand to teacher her fingering,
When, with a most impatient devilish spirit,
“Frets, call you these?” quot she, “I’ll fume with them.”
And with that word she struck me on the head,
And through the instrument my pate made way;
And there I stood amazed for a while,
As on a pillory, looking through the lute,
While she did call me rascal fiddler
And twangling Jack, with twenty such vile terms,
As had she studied to misuse me so.
According to Kahn,
the language in which her music lesson with Hortensio is described conveys the idea that it is but another masculine attempt to subjugate woman. . . . Later Petruchio explicitly attempts to “break” Kate to his will, and throughout the play men tell her that she “mistakes her frets”—that her anger is unjustified.
Katherine, then, is not merely a “shrew,” but a woman who is, in a sense, in rebellion against cultural norms. As such, there is chaos in her life and in the lives of those around her.
 Ibid., 1.1.57-58.
 Ibid., 1.1.61-65.
 Coppélia Kahn, “‘The Taming of the Shrew’: Shakespeare’s Mirror of Marriage,” Modern Language Studies 5, no. 1 (Spring, 1975): 93.
 The Taming of the Shrew, 2.1.149-159.
 Kahn, 93.