I am unsure if its true that there are certain breeds that do this or if its a myth.

pit bulls...they like to pick on the small and weak....lol

Some dog breeds catch mice and rats . . . my mum's mini foxie used to catch them, chew them up and leave the result on the welcome mat. She never had a single mouse in the house!. . . on the other hand I have a fluffy little pomeranian who wags his tail when he sees one, thinking it's his friend.You could be right about the breeds.

Terriers are, historically, good ratters, but, no dog is a good ratter unless they have been brought up being one. In fact, cats don't even make good ratters unless their mother taught them how. But, with training, you could teach your dog how to go after rats. I had a golden lab who loved going after all rodents.

I know that Schipperkes were originally bred to be "ratters" and watchdogs on boats. I'm not sure if they still have the natural instinct to catch rats though.