Why was Katherina's father putting off Bianca's marriage in spite of excellent offers in The Taming of the Shrew?
Good question, and I think there's a good answer. Two things keep Baptista from marrying off Bianca despite the many excellent offers you mention.
First, it would have defied the tradition of the eldest marrying first. Even in Biblical times, older daughters were typically married before the younger ones. (For example, in the story of Jacob, who wanted to marry the younger and more beautiful daughter Rachel, the girls' father tricks Jacob into marrying Leah, the eldest daughter.) It was sensible to try to do this, I suppose; however, the tradition has certainly not carried forth to this time.
The second reason is much more practical--and adds to the humor of the play. Baptista knows marrying this particular eldest daughter is going to take a minor miracle. He decides to use Bianca's marriage as leverage to find Katherine a husband. In other words, he's bribing/enticing/tempting them to find a suitable (or perhaps just a breathing)suitor for Kate if they want a shot at Biance. She's his bait.
One of the great ironies of The Taming of the Shrew is that Kate's marriage will be much more satisfying than Bianca's, despite its rocky inception.
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