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.