A rat terrier in fact all terriers instinct is to kill any small animal that moves. About 45 years ago I owned a pair of Feist squirrel dogs. They were good about keeping chicken killing vermin out of the main run, but they could catch and kill chickens faster than a fox.
If I caught them killing a chicken and whipped the dogs for it, they must have thought that I was punishing them because they weren't killing my chickens fast enough to suit me. One day I heard a commotion and one of the dogs came around the corner of the fence with an escaped hen in her sights. On instinct I grabbed up a stick laying there and bopped her on the head. The dog yelped and fell over kicking like she was "Grave yard dead." Without enough time to think it through, I scooped the dog up and soused it down into a 55 gallon barrel of freezing rain water. The icy bath had a bad effect on the pooch, it snapped it out of its dying trembles. That was the worst good deed that I ever did. Soon after that I gave both dogs away.
There are three types of training. Positive reinforcement training which works for thing like "Sit Rover" or "Roll over Spot" followed by a reward.
Negative reinforcement training which earns the pooch an immediate punishment for observed bad behavior.
The third type is aversion training which is intended to break bad habits, behavior that the dog may not know is Verboten, but that its owner can not easily catch the pooch committing. Bad aspects of a dogs' instinct falls into this realm. Aversion training is not cruel on its face, nor is it "retroactive" punishment, it is just another tool in the dog owner's tool box. Think of aversion training like the little boy who steals a quid of his pappy's chewing tobacco and is deathly sick for his troubles. The idea is that the little boy associates his stomach discomfort with the chewing tobacco and not with his father.
Besides, I don't think anyone here has yet weighed in on how cruel it is to maintain a pack of or even one chicken killing k9 in the midst of a flock of chickens.
Before handing me my own aversion training my old man used to tell me "Son, this is going to hurt me worst than it is going to hurt you." I have to say though that my father took my whippings like a man, I never once saw him cry.