If you read the story, it is all about taming Katherine. Now why would she have to be ‘tamed’ if someone didn’t think she wasn’t subservient enough, or demure enough, or enough of any of the other things that a ‘lady’ was supposed to be five hundred years ago.

If you seriously don’t know what sexism is all about, you better do some intensive reading to find out, or you are apt to be on the receiving end of it, not liking it, and not realizing what the problem is.

2. discrimination or devaluation based on a person’s sex, as in restricted job opportunities; esp., such discrimination directed against women.

This shouldn’t be too hard to find in older literature. I mean they didn’t even allow women to play women back in Shakespear’s time, it was all men up on the stage. If you have read the story, look for remarks that make women look bad or as if they do not equal up to a man position in life and you will have your answer.