John Steinbeck had to work out the plot for his novel before writing it. One thing he probably had in mind at the outset was that he wanted to end the story with one man killing his friend out of compassion. The author needed to establish that George had access to a weapon, but it could not be a weapon that George actually owned. Why not? Because if Lennie were killed with a weapon known to belong to George, then George could be arrested and convicted for murder. Steinbeck must have invented the character of Carlson primarily to establish the existence of a suitable weapon, a German Luger, which is a very distinctive-looking automatic pistol. When George pulls the Luger out of his coat pocket in the final chapter, the reader is expected to recognize it as the one that was missing from George's bunk at the ranch.
Steinbeck planned to turn his short novel into a stage play (see the Introduction in eNotes Study Guide via reference link below). The book is written in such a way that it could obviously be adapted into a script with a minimum of time and trouble. For example, there is hardly any prose exposition in the book. The characters provide information for the reader and the future audience through their dialogue. To take another example, the book is extremely short, suggesting that the author's intention was to make everything fit into the dimensions of a stage play lasting only around an hour and a half. The "shotgun ending" of the story brings it to a conclusion; otherwise a story about the hard lives of farm workers could go on indefinitely. The ending puts a "frame" around the story.
Carlson is a middle-aged man. He probably owns the Luger because he served in World War I and either took it from a captured German officer or bought it from another soldier. Carlson keeps the handgun partly as a souvenir and partly for protection. Life was dangerous for itinerant farm workers during the Great Depression. Candy probably owned a dog for the same reason that Carlson owned a pistol. It was dangerous to be riding on freight cars with strangers, dangerous to be sleeping in hobo jungles, dangerous to be tramping the highways, and dangerous to own anything of value. George probably kept Lennie as a buddy for protection as well as for companionship. Lennie was a big, powerful man who would do anything George told him to do.
When Carlson shoots Candy's dog, George learns how to kill quickly and painlessly with a pistol. He also observes how Candy works the mechanism when he cleans the weapon after using it on the dog. And he sees where Carlson keeps it under his mattress. The weapon George uses to kill Lennie had to be a pistol because George had to keep it concealed.
Carlson is a bitter man. He didn't expect to end up doing back-breaking farm labor for room and board plus fifty dollars a month in wages. The smell of Candy's dog irritates him because it reminds him of his miserable existence. He is angry at the world and takes it out on the old dog.
While Carlson is speaking to Slim (in chapter two of John Steinbeck's Of Mice and Men), he states the many reasons that Candy's dog needs to be put down.
First, Carlson states that the dog is so old that it cannot walk any longer. Second, he states that the dog "stinks like hell." Carlson goes on to elaborate on the dog's smell stating that he can tells the dog has been in the bunk house for days after because the bunk house stinks for two to three days. Third, the dog does not have any teeth. Fourth, the dog is almost blind. Fifth, the dog can no longer eat solid food; Candy gives the dog milk.
Later, in chapter three, Carlson gives two more reasons why the dog should be put down. First, the dog is "stiff with rheumatism." Second, Carlson says that the dog is no good for Candy. Lastly, he states that the dog is "no good to himself".
The following is an excerpt from eNotes study guide for Of Mice and Men:
"Candy comes in, followed by his ancient dog and Carlson, who has just lost at horseshoes. Carlson immediately starts to complain about the smell of the feeble old dog and tells Candy that he should shoot it and take one of the new pups in its place. Candy is reluctant, but Carlson offers to shoot the dog himself and, after some deliberation, Candy agrees that it must be done"
Carlson want to shoot the dog because he is so old he can no longer walk or perform basic actions such as eating in order to survive. Carlson has just lost a game of horse shoes and is irritable. His bad mood is exacerbated by the smell of the dog. He rationalizes his desire to shoot the animal by telling Candy that it no longer serves it purpose, and can be replaced by one of the younger dogs. This moment is sadly reminiscent of the way that individual's treated Lenny. Lenny was prized for his strength and ability to work, but like the dog unappreciated as a being beyond fulfilling this work purpose.
The entire study guide can be found at the link below.
Carlson wants to shoot Candy's dog beause he is old, ill, smelly, and a hinderance to have around to feed. These reasons justify the shooting because Carlson only wants to end Candy's dog misery.
Carlson said thoughtfully, “Well, looka here, Slim. I been thinkin’. That dog of Candy’s is so God damn old he can’t hardly walk. Stinks like hell, too. Ever’ time he comes into the bunk house I can smell him for two, three days. Why’n’t you get Candy to shoot his old dog and give him one of the pups to raise up? I can smell that dog a mile away. Got no teeth, damn near blind, can’t eat. Candy feeds him milk. He can’t chew nothing else.”
This is why Candy never wanted to kill his dog.
Well, I can’t stand him in here,” said Carlson. “That stink hangs around even after he’s gone.” He walked over with his heavy-legged stride and looked down at the dog. “Got no teeth,” he said. “He’s all stiff with rheumatism. He ain’t no good to you, Candy. An’ he ain’t no good to himself. Why’n’t you shoot him, Candy?”
The old man squirmed uncomfortably. “Well—hell! I had him so long. Had him since he was a pup. I herded sheep with him.” He said proudly, “You wouldn’t think it to look at him now, but he was the best damn sheep dog I ever seen.”
Carlson tells Candy this when he was about to shoot the dog.
Carlson was not to be put off. “Look, Candy. This ol’ dog jus’ suffers hisself all the time. If you was to take him out and shoot him right in the back of the head—” he leaned over and pointed, “—right there, why he’d never know what hit him.”