Katherine, also known as “Kate” or “Katherina,” is the titular character of William Shakespeare's “The Taming of the Shrew.” Her role is the factor that drives the story. In short, Katherine is the driving factor of The Taming of the Shrew and is the romantic foil for Petruchio, who is the male protagonist of the play. Without Katherine, there would be no story for The Taming of the Shrew. In the story, Katherine juggles the three roles of titular female character of the story, the romantic foil to the male protagonist, and the main obstacle course.
In the story, there are several men who want to marry the beautiful Bianca who is Katherine's younger sister. Katherine's “shrewish” personality is the necessary driving force behind the story. She is violent, temperamental, scolding, nagging, and venomous. In short, Katherine is an abrasive person who repels potential suitors. Because of that, Katherine has yet to be married. This brings forth the important plot device of traditional family marriages. Before the younger daughters can be married off, the eldest daughter has to be the first to get married. If not, then the other daughters cannot get married.
That makes Katherine the biggest obstacle to Gremio, Lucentio, and Hortensio who all are interested in marrying Bianca. They have to get her out of the way. Petruchio comes into the picture because he ends up being the one who marries Katherine. It works out for almost everybody as the suitors get Katherine out of the way and Petruchio ends up marrying into a fortune.
As the story progresses, after the marriage, there is a “fight” between Katherine and Petruchio. While she could be considered a shrew in the past, she would be considered a feminist today. Katherine is a very strong-willed woman who might be looking for someone who is her “equal.” She does not want someone to try to overpower her, nor does she want someone to be submissive to her. One can say that she is very aggressive and is forced to be in a passive state due to being married to Petruchio. Throughout the story, it is an interesting form of passive-aggressive behavior.
One can compare Katherine to hard and soft style martial arts. Hard style martial arts tend to focus more on force and strength, while soft style martial arts tend to focus more on flow and proper technique.
Keep in mind that the Taming of the Shrew was made centuries ago. During that time, society and women's rights were different. Since then, culture and society has changed. One can say that Katherine was ahead of her time. Petruchio, today, represents the oppression caused by a powerful male society. While she is considered a “shrew,” Katherine should be considered to be ahead of her time. Today, Katherine would be hailed a hero. In a sense, Katherine does represent an aspect of radical feminism.
In this regard, one can say that another driving force is Katherine changing from aggressive to assertive. Without Katherine, there is no shrew. Without a shrew to tame, then there is no Petruchio. Without either, then there is no Taming of the Shrew.