think Shakespeare used Bianca to somehow explain the reasons for Katherina's mistreatment. Katherina didn't behave like a "normal" Elizabethan woman and Shakespeare made Bianca behave like one to show the difference between what was accepted as appropriate behaviour and what wasn't.
             Shakespeare gives us brief stage directions prior to their entrance "Enter Baptista with his two daughters Katherina and Bianca; Gremio, a pantaloon..." straight away we can't take Gremio seriously because he is described as a pantaloon – a ridiculous old man whose role was to be an obstacle to young lovers marrying. As any woman would, Katherina was frustrated and insulted with the way the men talked about her as if she didn't have any feelings or even as if she wasn't there. Baptista says in Act 1 Scene 1:
             "That is, not to bestow my youngest daughter
             Before I have a husband for the elder
             because I know you well and love you well,
             Leave shall you have to court her at your pleasure".
             What Baptista is saying is that if either of those men are interested in Katherina they can have her. She is being treated as his property. Although this was the norm, we as a 21st century audience may think it's outrageous behaviour, but in fact that's how all fathers behaved if not worse. Gremio replies even more degradingly, "To cart her rather! She's too rough for me." He refers to her as a convicted prostitute and doesn't have any problem in saying it aloud in front of Katherina's father. This was very insulting for Katherina, however, she must have provoked Gremio in some way for him to be so angry at her, the exclamation marks used by Shakespeare create an impression that Gremio is angry and shouting. Katherina's behaviour would have been unseemly and therefore given Gremio the opportunity to see her as a shrew – a bad tempered nagging woman o...