Why do you think Petruchio compliments Kate, even when he is telling her what to do in Act III Scene II of The Taming of the Shrew?"But for my...

This is an interesting question to consider. We need to
take this quote in context and realise that this is Petruchio's most important moment in
his attempt to "tame" his shrew of a wife. She has just defied him publicly when he said
that he and his wife must leave that night when she
said:

For me,
I'll not be gone till I please myself.

'Tis like you'll
prove a jolly surly groom,

That take it on you at the first
so roundly.

The audience
excitedly anticipate a true fight as the bride and groom get used to the ways of each
other, yet Petruchio simply restates his command that Katharina go with him. Perhaps the
compliment is there to soften the bitter pill of his authority, or perhaps he is being
sarcastic (he has been so before). The text does not make it clear, however, just after
he calls his wife "bonny," he makes it evidently clear, addressing both his wife and the
guests, that now she is married to him, she is considered his
property:

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Nay, look not big, nor stamp, nor stare, nor
fret;

I will be master of what is mine
own.

She is my goods, my chattels; she is my
house,

My household stuff, my field, my
barn,

My horse, my ox, my ass, my
anything;

And here she stands, touch her whoever
dare.

This is a very famous
quote from the play that talks about the rights of man and how they "own" the women they
are married to. This is an authority that cannot be argued against, as Kate discovers as
her husband and Lord shames and humilates her into
submissiveness.