In The Taming of the Shrew what is the problem?

In "The Taming of the Shrew," the central problem revolves around the challenge of marrying off Katherina (Kate), a headstrong and outspoken woman, to a suitor, due to her reputation as a "shrew." Her sister, Bianca, is sought after by multiple suitors, but their father insists that Kate must marry first. The play explores themes of gender roles, obedience, and the dynamics of marriage as Petruchio takes on the task of "taming" Kate to make her a more compliant wife. This conflict raises questions about identity and the nature of love within societal expectations.