I really don't think people realize how hard it is to rehome a dog that chases/ attacks livestock. Its really darn near impossible even if the dog is the SWEETEST thing EVER to people. And like Absit clearly stated, sometimes you can try and try with a dog, and they just refuse to learn, or they go back to doing what they are doing.
I live on a farm and because of that I want a dog that is going to stick around and is going to be a good enough dog that I don't have to keep them kenneled or tied up...if you have to do that, it defeats the purpose of a farm dog. Fritz (my red heeler) Is really not my favorite dog... she has been so hard headed and she has an obnoxious personality- the only way that dog learns anything is through PAIN. Even then she likes to revert back to stuff she has gotten in trouble for a million times.. the only reason I tolerate her is because she does stick around, and she is a fantastic guard dog ( aloof to strangers BUT NOT aggressive), and while the bizatch will still occasionally nip a horse or tear something up , I KNOW she isnt down there terrorizing them when im not around. BUt if the need ever arises to where she would have to be "rehomed", I may as well put her down because NO ONE will want her.