In Of Mice and Men, how and why does Carlson say Candy's dog should be shot?

Carlson says that he will shoot Candy's dog in the back of the neck where the neck and head meet.  If he shots the dog at this place, he tells Candy that the dog won't feel anything.  He won't know what hit him.  Candy suggests doing this because the dog is old, smells, and is crippled.  Carlson says the dog isn't good to himself or anyone else.  He believes that dog is suffering, but Candy says that he has had hin so long that it is hard to get rid of him.  Candy's dog is his best companion.