Although "Of Mice and Men" appears to be a naturalistic, or realistic, story, it is actually heavily plotted. Steinbeck started off wanting to write a story in which one man ends up killing his best friend. His basic reason for wanting to end his story this way was to shorten it and bring it to a swift conclusion. A realistic, or naturalist, story about the lives of farm workers could go on indefinitely and not even come to a conclusive end but just sort of trail off. Steinbeck, as the eNotes Study Guide tells us, had an opportunity to turn his novel into a stage play to be produced in New York, the cultural capital of America. A stage play could not last for more than a couple of hours, and so Steinbeck wrote a novelette which is obviously unusually short in order to make the adaptation to the stage quick and easy. Both the book and the play came out the same year, in 1937. Both were quite successful and made Steinbeck famous.
Too much is probably read into Carlson's shooting Candy's dog. The main purpose for this episode was most likely to establish that a gun was available to George when he decided to kill Lennie. George would have no other way of killing his friend. For one thing, Lennie was much bigger and stronger. George could end up getting killed himself if, for example, he tried to kill Lennie with a knife or to hit him over the head with a big rock.
Carlson's gun is a German Luger. This is a very distinctive-looking foreign pistol. When George will pull it out of his pocket in the stage play, everybody will understand that he took it out from under Carlson's bunk when he left to meet Lennie by the river.
Carlson found a little cleaning rod in the bag and a can of oil. He laid them on his bed and then brought out the pistol. took out the magazine and snapped the loaded shell from the chamber. Then he fell to cleaning the barrel with the little rod. When the ejector snapped, Candy turned over and looked for a moment at the gun before he turned back to the wall again.
George has an opportunity here to see how this German pistol works. Everybody knows that Carlson owns the gun and where he keeps it. Everybody has heard Carlson tell Candy how he can kill the old dog painlessly, by shooting it at a certain place in the back of the head. All of this goes to showing George where the gun is kept, that it is loaded, how to use the ejector to jack a shell into firing position, and even where to point the gun at Lennie in order to kill him painlessly at the end.
It would not do for George suddenly to pull a pistol out of his pocket without ever establishing where he would have been able to get it. Steinbeck could have specified early in the story that George owned a gun himself, but if he considered doing that when he was plotting his story, he would have rejected the notion because it would have given the audience an early warning that he probably was going to use it. Besides that, it would not seem in character for George to be carrying a gun, whereas it is obviously very much in character for Carlson to own a gun. And furthermore, if George killed Lennie with his own gun he would be much more in jeopardy of being charged with murder. The men in the bunkhouse all see that Carlson's gun is missing before they leave to track down Lennie, and they all assume that it was Lennie who took it.
Carlson is a middle-aged man, and his surly nature is partly due to the fact that he has no future except for more hard work and living in a bunkhouse with a bunch of losers and sleeping on a burlap sack filled with barley. He was probably a soldier in World War I and brought the Luger back as a souvenir, as did so many soldiers after the Great War. He keeps it partly for sentimental reasons; it reminds him of his youth and the one great adventure of his life. He also keeps it for protection in the dangerous world of homeless men who sleep in hobo jungles and travel in railroad boxcars.
If there is any symbolism in Carlson's killing Candy's dog, it is only incidental and secondary.
The world these men live in is an unsympathetic one and a world were there is no room for sentiment and attachment. Candy has had his dog his the dog was a puppy; the dog is probably the only true friend Candy has. However, since the dog is no longer useful or beautiful, Carlson argues that the dog should be shot and put out of its misery. Candy finally agrees to it, though it is a difficult decision for him to make. This relates to many things we see today--old, beautiful building get torn down because we need something more modern, many older people get put into homes or assisted living facilities because we have no time to take care of them and the issues they may bring with them.
The dog is also a symbol for Lennie and Candy is a symbol for George. Though Lennie and George have an unusually close friendship for men in this era, Lennie is constantly getting himself and George in trouble and kicked out of jobs. George needs to make the decision as to whether he will kill Lennie or let the angry mob, led by Curly, take his friend's life. Rather than have the same regret Candy did about not being the one to kill his dog, George takes the matters into his own hands, and puts Lennie out of his misery and save him from misery yet to come.