Whipped as a dog, one may be a cat! (3)

I believe the answer is:

pet

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'a cat' is the definition.
(cat is an example of a pet)

I don't understand how the rest of the clue works.

(Other definitions for pet that I've seen before include "Tamed animal; sulk" , "Favourite - maybe teacher's" , "A dear one exhibits sulkiness" , "Caress or fondle, as with favourite" , "House animal; sulk" .)

I've seen this clue in the Evening Standard.

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