Kate is the title character (the "Shrew") of the play. The eldest and unmarried daughter of Baptista Minola, no man wants anything to do with her because she's got a hot temper, slaps people around when they make her mad, and shreds men to bits with her razor sharp tongue. Her knack for verbal repartee and ability to call it like she sees it reveals her incredible wit and intelligence, which we can't help but appreciate.
What? You want more specifics? OK. Kate yells at her father in public, ties up and beats on her little sister Bianca, throws tantrums and claims her dad doesn't love her, breaks a musical instrument over the head of Hortensio, and insults everyone she meets.
Her behavior is obnoxious, to be sure, but we need to think about why Kate acts the way she does. Her dad seems to think she's just innately nasty. When she weeps and rails because she thinks Petruchio has stood her up at the alter, Baptista says something to the effect that he can't blame Kate for being angry – she's an impatient shrew, after all (3.2.2). It never occurs to Baptista that Kate might be upset because she's being publicly humiliated and feels hurt.
In fact, the play invites us to see Kate from the point of view of men who see only a monstrous stereotype. Our first look at Kate is through the eyes of Lucentio and Vincentio, who says, "That wench is stark mad or wonderful froward" (1.1.3). At the beginning of the play especially, we often hear more about Kate than we hear from her (though we certainly do hear from Kate). Her reputation as "curst," "shrewd and froward," "a devil," and a "mad" wench circulates among Bianca's suitors, who are happy to pass along the information to Petruchio before he even meets Kate. This colors his impression (and to some extent ours) of Kate before Petruchio ever lays eyes on her.
So, why does our girl act like such a shrew? Is it because she's just inherently obnoxious like her dad says? We know Baptista doesn't know the first thing about his girls – he thinks Bianca is an angel for Pete's sake – so let's not take his word for it. How about this: Kate is a really smart woman with a mind of her own. She doesn't fit neatly into the social role prescribed for upper-middle class women in the 16th century (silent, obedient, baby-making, husband-pleasing machines), which makes her a social outcast and drives her violent and surly behavior.
Our evidence? Well, to start, the first time Kate speaks (or shouts) in the play is when she objects to her father's behavior when he breaks the news that Bianca can't get married. Get a load of this:
If either of you both love Katharina,
Because I know you well and love you well,
Leave shall you have to court her at your pleasure. (1.1.1)
Translation: "Hey, guys, my youngest girl isn't on the market right now. But, I like both of you guys a whole lot so, if either one of you thinks my oldest girl is hot, feel free to have a go at her. I'm sure we can work out a deal." Who can blame Katherine for not wanting to be treated like a piece of meat, a mere commodity to be traded?
Does this mean Kate is opposed to marriage altogether? Not necessarily. It's true she claims she's not interested in getting hitched when she threatens to bloody Hortensio's face with a chair (1.1.2). But this may be a defense mechanism to protect herself from Hortensio's claim that she will never land a guy because everybody hates her. It's also her way of saying she's not interested in marrying a clown like Hortensio. Later, though, it seems plausible that Kate is interested in love when we consider why she ties up and slaps Bianca.
Of all thy suitors, here I charge thee, tell
Whom thou lovest best: see thou dissemble not (2.1.1)
Here, Kate just wants to gossip with her little sister about Bianca's boyfriends. It also seems that she wants to live vicariously through Bianca and is far more interested in marriage than she lets on. When the passive aggressive Bianca implies Kate is an old maid and condescendingly offers to let her have any one of her suitors, Kate responds in the only way she knows how – with physical violence.
We know that Kate's bad behavior involves lots of slapping, foot stomping, and hog-tying annoying siblings. But, the play suggests the biggest problem is Kate's mouth. She just won't keep it shut and, when she speaks, nothing nice comes out of it. This is a big no-no for any girl living in 16th century. This is why the largest part of Petruchio's task to "tame" Kate is to control what does and does not come out of Kate's mouth – her speech.
After Kate marries Petruchio, her only means of expressing her anger and frustration over her limited social role is through language. (Once married, women basically lost all legal rights and had no identity of their own. This is why Petruchio refers to Kate as his "goods" and his "chattels" after their marriage ceremony.) Observe:
Why, sir, I trust I may have leave to speak;
And speak I will; I am no child, no babe:
Your betters have endured me say my mind,
And if you cannot, best you stop your ears.
My tongue will tell the anger of my heart,
Or else my heart concealing it will break,
And rather than it shall, I will be free
Even to the uttermost, as I please, in words. (4.3.12)
When Petruchio refuses to let Kate choose her own clothing and tells her to pipe down about it, Kate objects to his attempts to shut her down. Here, Kate suggests the act of speech can alleviate one's pain and suffering. She also says that her heart "will break" if she is silenced and unable to express her frustration about her lack of power and control over even her own wardrobe. Rather than endure such suffering (here, she implies that it causes a kind of physical pain that will literally destroy her on the inside), Kate refuses to keep her mouth shut.
So, what the heck happens between this moment and Kate's final and most puzzling speech at the wedding banquet (5.2.6)? Well, we know that Kate finally breaks, or gives in to Petruchio's haranguing on the road to Padua (4.5.3). It seems pretty clear that Kate decides then and there to play along with Petruchio's antics. Critics often point out that this is the moment Katherine becomes an actor – a woman capable of role playing (she pretends the sun is really the "moon" and then pretends that an old man is really a "budding virgin" to make Petruchio happy).
This lends itself to the idea that Kate's last speech, where she calls Petruchio her king, is also just an act that ensures some kind of domestic tranquility. This is a far more appealing option than the idea that Kate is merely a broken-down, brain-washed woman at the play's end. Still, it's important to remember that Kate is never given any other choice. Like Bartholomew in the Induction, Katherine is ordered by her "master" to act the part of "good wife." You can go to "What's Up With the Ending?" if you want to think about this some more. Also, if you want to see a bit of analysis of Kate's witty back and forth dialogue with Petruchio, go to "Writing Style." For now, our work here is done.