Kate is the oldest, and she should be married off before Bianca. Baptista wants to see both of his daughters well matched, but, even though he puts Bianca's suitor's officially on hold, he doesn't hold much hope for finding a good match for Kate. (Even when one comes he tries to tell him that he doesn't really want her). Does he care about his daughters' happiness? Sort of. He seems, however, befuddled by Kate. When an offer comes, he takes it, completely disregarding Kate's feelings on the matter.

He seems to care more about money than about his daughters' emotional well-being. An Elizabethan audience might be more sympathetic toward this position than a modern one. To us, he seems shrewd and calculating, especially when he gives Kate's hand away against her will.

It's probably also important to note that Baptista understands how difficult Kate can be. He knows that he'll find a myriad of acceptable suitors for Bianca, which is why he restricts her dating until Katerina has a match. Knowing how difficult it will be to get her married, he quickly jumps at the chance to join her with Petruchio.

Baptista's main concern is his daughters. Everything he does in "Taming of the Shrew" is for his daughters. Some may say that he doesn't consider his daughter's feelings in making matches for their future, however, he is doing the only thing he knows that will make them secure in the future; finding appropriate, financially secure suitors.