Why do they call cat burglars cat burglars if they do not steal cats?

No! Of course not. It's just a figure of speech. Cat burglars creep around, mostly at night, as they "case" offices and homes with the intent to break in and burglarize the places. They are known to be "silent as cats", hence the "cat burglar" moniker. Sometimes, cat burglars are so quiet, they can break into homes while the residents sleep and the homeowners never see or hear the burgular.