Just to take a simpler route to answer this question all in good fun, I would say that Bianca isn't a shrew at the beginning but becomes one in the end because she is a dynamic character and was designed to be that way by Shakespeare. Although some critics disagree with me, I think of Bianca as a sort of foil to Katharina. They go through their dynamic changes directly opposite of each other: Katharina turning from shrew to loving female and Bianca turning from loving female to shrew. I have to admit, though, I don't usually describe Bianca as a "shrew" at the end of the play. Still, anger can certainly make a lady quite ugly, can't it? Therefore, in speaking of Bianca as a shrew, I suppose that if the shoe fits, ...
Kathrine is considered the shrew in the title because she refuses to be ruled by her father.
In Kathrine's world, her father would choose her husband. Love was not a part of the equation. What was important was a "good" marriage. Family connections and how much money was involved were also all important. It is a male dominated world and Kathrine wants nothing to do with it all.
Bianca, on the other hand trusts that her father will marry her to the man she wants since she has him wrapped around her little finger. Once she gets what she wants she doesn't have to pretend any more. She shows her true colors. (Her name means white.) In a sense, she has been dishonest whereas her sister has been honest to a fault.
Basically, Kathrine rebels against the male dominated world she lives in whereas Bianca submits to it.
Good question. Since we aren't told this directly, we must deduce our answer from the action of the play. I would say it is because of three things. First, the focus has shifted. She was the good one, and Kate so shrill that no one could see her beauty. Now that Kate is good, her beauty is visible, and Bianca is mad. Second, the structure has shifted. They aren't both competing for their father's approval and that of unmarried men; they are showing off as wives, and the criteria are different. Third, Petruchio is more impressive in the end than her husband, and some of that glory reflects.
yes you are right and that is because Katherine (when she was a shrew ) was learnt how to be tamed by Patruchio her husband... when he married her , he insisted to tame her by making the opposite of what she wanted saying that those deeds were for his love towards her ( like :shouting at the dress and hat makers declaring that their products were not good ones although they were made according to the fashion during that time)
Bianca was believed to be the tamed daughter of Baptista but at the end she proved quite the opposite by refusing to come to her husband when he ordered her to do so on their wedding day thus her husband said :"I wish your duty were as foolish too!The wisdom of your duty,fair Bianca, has cost me a hundred crowns since dinnertime."
So Patruchio was right and Katherine was a good lady and maybe her shrewish character was because she didn't know how to improve it while Bianca's character was a bad one hiding itself behind untrue words.
Moral lessons: we must compare between promises and actions ,,, live in peace & love eachother to lead a quiet life.
That's a great question. Well if you were to consider the theme that the Christopher Sly Induction introduces to us: that people aren't always what they seem; it completely changes the tone of the rest of the piece. So by this token, we can conclude that Bianca was most likely putting on an act in order to garner the attentions of her suitors and father. Taking this into consideration might explain a bit more of Katherina's interactions with her sister. Katherina sees through her sister's superficial exterior and is frustrated that others--especially her father--do not as well. However the reason why they didn't notice it probably has more to do with the Renaissance belief that those who had beautiful exteriors must also have beautiful interiors as well. Bianca reveals that she isn't in actuality when at the end, after she has achieved the the comfort of a marriage that will last until she or her husband dies, and therefore can afford the luxury to expose her true nature at the end of the play, when before she had to play a part to ensure she could keep her father's favor and get the best suitor she could.
Below are some links which help explain this interpretation further.