Baptista: If either of you both love Katherine,
                    Because I know you well and love you well,
                    Leave shall you have to court her at your pleasure.
  Gremio: To cart her, rather. She’s too rough for me (1.1.52-55).

In this exchange, Baptista offers Katherine’s hand in marriage to Gremio and Hortensio. Gremio immediately refuses because of Katherine’s tempestuous nature, which he and the other men in the text view as unladylike. Shakespeare, through Gremio’s pun, establishes that Katherine is undesirable because she refuses to subscribe to socially enforced gender roles. He puns on the word “court” and says that he would rather “cart” Katherine than “court” her. Gremio is referring to the Elizabethan practice of tying disorderly women to a cart and parading them through the streets for public ridicule.

“No mates for you, / Unless you were of gentler, milder mold” (1.1.59-60). 

This line is spoken by Hortensio shortly after Baptista offers Katherine’s hand in marriage to Hortensio and Gremio. Like Gremio, Hortensio is uninterested in Katherine because she does not behave in the gentle manner that society enforces on young women. However, Hortensio takes Gremio’s refusal a step further and rejects Katherine to her face instead of merely addressing her father. This is a crucial moment in the play because it is the first of many times that a male character tells Katherine that she is not behaving the way a woman is supposed to behave.

“Go ply thy needle; meddle not with her” (2.1.25).  

This line is delivered by Baptista to Bianca when Baptista intervenes in a fight between his two daughters. His attempt to comfort Bianca is important for two reasons. One, he immediately takes Bianca’s side and even refers to Katherine as a “devil” in the following line, revealing the dynamic within the family unit. And two, Baptista comforts Bianca by suggesting that she leave to work on her needlework, an activity associated with traditional femininity. As a result, Shakespeare emphasizes that Bianca is Katherine’s mild-mannered foil who adheres to the socially mandated and maintained gender roles that Katherine rejects. 

“This is a way to kill a wife with kindness.
    And thus I’ll curb her mad and headstrong humor.
    He that knows better how to tame a shrew,
    Now let him speak; ’tis charity to shew” (4.1.189-192). 

Petruchio delivers these famous lines during his speech in 4.1, in which he compares his plot to tame Katherine to the act of domesticating a wild falcon. He explains that Katherine will only become an ideal wife once she learns to curb her combative disposition and submit to his will. In this line, then, Petruchio explicitly states that, according to him and the other men in the play, there is a correct and incorrect way to act like a woman within society.

Katherine: And gentlewomen wear such caps as these.
    Petruchio: When you are gentle, you shall have one too, 
                       And not till then (4.3.71-73). 

This exchange between Katherine and Petruchio occurs after they are married. Petruchio is playing one of his tricks on Katherine and pretends that the beautiful gown that Katherine is admiring is incorrect and refuses to let her wear it. The language in this interaction is crucial to understanding the play’s emphasis on gender roles. Katherine wishes to wear the gown but Petruchio insists that she can only wear a gown befitting of a gentlewoman once she adopts a more gentle manner. Here, Petruchio essentially says that Katherine only deserves women’s clothes if she acts like one.