What does the killing of Candy’s dog reveal about Candy, Carlson, and Slim?

It reveals that Candy felt helpless when it came to killing his dog. Candy holds no power on the ranch and Carlson's reason's for euthanizing the dog made sense. Carlson was not trying to be cruel but his practicality comes off as unfeeling. Slim is the final decision maker. He nods his head and Candy knows it has been decided. I think Slim understands Carlson's points about Candy's dog being a liability. Slim tries to appease Candy by offering a pup from his litter.