The theme of appearance vs. reality seems to be an omnipresent theme in many of Shakespeare's comedies, and this excellent play is no exception. Of course, in this scene, Act III scene 2, the discrepancy between these two states is in the role that Petruchio plays as a new husband, and how he commands (and shames) his wife, inventing an excuse to deliberately "tame" her from her shrewish ways and giving him ample opportunity to state his authority over her as her husband. Note how Petruchio is quick to inconvenience Kate and deliberately provoke a response from her:
I must away today, before night come.
Make it no wonder. If you knew my business,
You would entreat me rather go than stay.
It is impossible to imagine a bridegroom insisting on leaving with his bride before their wedding feast, and even before she is able to bid farewell to friends and family, but Petruchio does this, and in addition, leaving in such a mad state as to embarrass Katharina and humiliate her:
Draw forth thy weapon; we are beset with thieves.
Rescue thy mistress, if thou be a man--
Fear not, sweet wench, they shall not touch thee, Kate!
I'll buckler thee against a million.
It is hard to escape the conclusion that Petruchio is playing a deliberately artificial role as part of his campaign to tame his wife. Appearance is not what it seems, and the reality of Petruchio is carefully hidden until his campaign has been successful.