He has tamed her. Essay on Desire in The Taming of the Shrew, by William Shakespeare - People have always gone out of their way to obtain what they desire in their life. However, suitors who seek Bianca as a wife have to wait for her sister to be married first.
He hopes to capitalize on a handsome dowry, as Hortensio points out.
Using the same tactics to tame Katharina that he uses to tame falcons and hawks, Petruchio forces her to acknowledge that he is always right, even when he says the sun is the moon. It may also be that she was simply born mean.
If you look very closely at just one wire in the cage, you cannot see the other wires. Shakespeare indeed does transcend the stereotypes of his own time. Father of the two, Baptista Minola, fusses with potential suitors for young Bianca and will not let them come calling until his elder, ill-tempered daughter Katherine is married Frustrated, Katharina agrees: It is the moon.
To entertain themselves on the way, various pilgrims tell stories. But if he says it is the moon, she adds, then it is the moon. But she meets more than her match in Petruchio, who also uses language as a weapon.
And that is the dilemma that Renaissance women of the real world faced in Shakespeare's time.