What was Big Willy Shakes going for?
Petruchio sort of puffs out his chest and challenges the audience to come up with a better way to get a shrewish woman in line. He promises his way is "kind" because he's not actually beating her or anything. Right.
Starvation and mental conditioning don't sound too kind to us, but Petruchio's point is that he's got to break in or fix his woman. The Taming of the Shrew is not about the domestication of an actual "shrew" (the mammal Sorex araneus). Rather, the play's title refers to the way Petruchio breaks the will of the "shrewish" Kate. She's a stereotypically bossy, mouthy, and aggressive woman who is seen as trying to "wear the pants" in her relationships with men.
To Shakespeare's audience, this was a big no-no because women were supposed to be the more silent, submissive type back then. Elizabethans were really worked up about all the shrewish wives running around making their husbands look like wimps.
Okay, so what do we make of this? Aside from the fact that Petruchio can be seen as a jerk, we should think about how his character speaks to the idea that social roles are performative. In other words, getting along in the world requires one to do a lot of acting. Many critics point out that Petruchio teaches Kate how to play-act, to perform a role other than "shrew." This would make his "taming school" more of a nightmare theater boot camp than anything else.
Are we letting Petruchio off the hook? Nope. Some people think he's utterly abusive toward his wife and revels in his power over Kate. Others think that he's Shakespeare's way of sending up other versions of the shrew plot that were on the Elizabethan stage—versions in which the tamer beats the shrew into submission. Shakespeare wasn't having any of that.
It's possible that Big Willy Shakespeare leaves open the possibility that anyone who tries to follow Petruchio's advice and behavior is a total idiot. Hortensio, who spends a lot of his valuable time at Petruchio's so-called "taming school" (though he pretty much misses the entire point Petruchio is trying to make), winds up having absolutely no control over his wife, the Widow.
In fact, she ends up humiliating him when she disses him in public and causes him to lose a bet. Also, while it appears that Kate has been tamed, her final speech is so over the top that we wonder if Petruchio has trained an obedient wife or just a woman who has learned how to pretend to be obedient. If the latter is true, could this be what Petruchio intended all along? Hey, maybe he likes his woman "shrew-ish."
Either way, we appreciate the way the characters' obsession with acting and performing allows the play to acknowledge that social stereotypes (shrews, good girls, manly men, etc.) are not innate characteristics and are perhaps best left on the stage.