William Shakespeare’s play was written during an era of female oppression. Women were expected to be quiet and soft spoken and respectful of their fathers and husbands. The males dominated their environment and they were expected to be subservient to them. It was also expected that the older sister was supposed to marry before the younger sister could marry. The younger sister has many suitors who wan her hand in marriage.
In the play "The Taming of the Shrew" the primary character is a vicious dominating mouthy daughter who talks badly to everyone. She is also quite spoiled having advantages many other women could not afford. She takes orders from no one and scares off the male population. Her younger sister is the opposite. She behaves in the manner expected of the delicate aristocratic female.
The problem is that no one wants to marry Kate. She is such a shrew that she drives people away. Pertuchio comes along who she sees as her match and a way to gain a fortune. He is rude and seeking fortune. He decides that he will marry her because there is a large some of money to be paid as a dowry. He believes that he can tame her. Katherine knows she will tame him before he can tame her. Her father is relieved because she is off his hands, and now her sister can marry.
Both girls marry. Kate's husband has wealth but his house is lacking any female touch. At first Kate fights her way through the marriage. However, her husband, Pertuchio, manages to break her and when he does she finds real and deep love. They return to a castle for a visit. The irony is that Kate is now domesticated and demure and her sister and the other women are, though not a harsh as Kate was, demonstrating inappropriate behavior towards their husband (as defined by the social expectations of women).
Kate has become what was expected of the women of her day. Her husband has also changed and is no longer the rude man that she first married. He lavishes her with gifts and is good to her.