Quote 10
KATHERINE
Her silence flouts me, and I'll be revenged! (2.1.32)
Katherine and Bianca, like many sisters, have a tumultuous relationship. (Though, we don't know many women who have tied up their sisters and slapped them around, as Kate does in this scene.) We can't help but notice, however, that they never seem to make up or find any common ground and siblings or even women. Even at the play's very end, Katherine "scolds" her little sister (and the Widow). It's not just Kate, however, that can't play nice. None of the women get along, which is especially evident in a play where the men run around scheming together.
Quote 11
KATHERINE
What, will you not suffer me? Nay, now I see
She is your treasure, she must have a husband,
I must dance barefoot on her wedding day
And for your love to her lead apes in hell.
Talk not to me. I will go sit and weep
Till I can find occasion of revenge. (2.1.34-39)
Kate's accusation that Baptista loves Bianca the most sounds a bit childish, but it's not unfounded. Baptista does treat Bianca as a "treasure." This isn't the first time that word has been used to describe the way Baptista guards his youngest child. Hortensio sees Bianca as a "treasure" as well and accuses Baptista of being miserly with his "riches" (1.2.7).
Quote 12
PETRUCHIO
O Kate, content thee. Prithee, be not angry.
KATHERINE
I will be angry: what hast thou to do?—
Father, be quiet. He shall stay my leisure. (3.2.221-223)
This moment suggests that a daughter's relationship with her father is a good predictor of the kind of wife she will be. Kate is disrespectful to Baptista (we assume he has tried to interrupt Kate but she shuts him down before he can get a word in edgewise) and so, we can assume that she will be just as disobedient and disrespectful to her husband.