In The Taming of a Shrew, the shrew, Katharina, is repeatedly pictured not only as uninterested in men, let alone marriage, but also as a woman who always has something to say. So when, in scene 1 of act 2, Katharina clams up after making only one complaint about her proposed marriage to Petruchio, the effect is shocking and confusing for the reader. Katharina — outspoken, loud, shrewish Katharina — has nothing to say beyond, "I'll see thee hang'd on Sunday first!" (2.1.299) in terms of protest when Petruchio more or less forces marriage on her, and it's not immediately clear why. However, when one considers the time period in which the play takes place, and the reality that forms for Katharina if she never marries, her motivation for backing off becomes clearer. And on top of that, Petruchio treats her less like the monster all the other men treat her as and more like a human, and he manages to keep up with her.Petruchio's treatment of Katharina is a significant part of the scene. Katharina, had she wanted to marry any old man who came through, could have toned her attitude down and settled. But as she makes clear through her actions with Horatio and Gremio, she has no desire to marry just anyone, nor any desire to make herself more palpable as a wife. When Petruchio shows up and not only manages to keep up with her, but also never once insults her, as he planned in the previous lines, "Say that she rail; why then I'll tell her pain / She sings as sweetly as a nightingale:" (2.1.170-171), Katharina is surprised, to say the least. And when despite her very harsh and trying personality and protests, Petruchio maintains his interest, Katharina would likely sober up a bit and at least take the prospect of marrying him a little more seriously, especially since he is, as far as the reader knows, the only man to have shown an interest in marrying her.
Even more, Petruchio's stance does not shift, and he does not give in when Katharina says she'd rather see Petruchio dead than marry him, and both Tranio and Gremio follow her up by teasing Petruchio for acting as though he had wooed her. Rather, he asserts, "Is she and I be pleased, what's that to you?" (2.1.303). He doesn't just prove his diligence, but also that he does at least have some awareness that Katharina's happiness matters, even if he does immediately follow it up with a fallacious lie about how he and Kate have an agreement where she acts shrewish in public, but he cannot get her off him in private (2.1.305-310).
However, perhaps one of the most effective motivators for Kate is the fact that because of her gender and time period, marriage isn't exactly an option for her. Although she could choose not to get married, it would result in her living with her sister and her husband, or with her father and she would receive no inheritance and would become a spinster — a single older woman who was looked very poorly on. Not a very appealing prospect for anyone, even a shrew.
Although at first Katharina's silence is baffling bordering on out of character, with some deeper reading her reasoning and motivation become clearer. The idea that a single woman would not completely ruin her chances with a man who could quite possibly be her first and last suitor is not completely laughable, or even strange. Even a shrew who does not want a husband needs a husband if she intends to continue to live as a pseudo-independent woman — and Katharina knows this. All in all, Petruchio is nowhere near the worst choice she could make, and he does seem to enjoy her company, or at least be able to speak with her without stooping to insults.