In Of Mice and Men, Steinbeck wanted us to respond to the deaths of Candy's dog and Lennie with compassion. It is sad to become useless. Candy's dog had become useless. He had seen his better days. After all the years of contributing, it is sad to be in the way. That is how the ranch hands looked at Candy's dog. He was in the way. He was useless. So he had to be shot.
In much the same way, the ranch hands looked at Lennie as a trouble maker. He was in the way. He did not serve a positive purpose. He caused trouble everywhere he went:
Lennie dies because he is incapable of living within society and is in fact a menace. His contact with living creatures, from mice to puppies to Curley's wife, results in destruction.
The reader looks at Candy's dog and Lennie in another way. They are both very special. Candy's dog had been a faithful companion for years. Candy relied on his dog. In much the same way, George relied on Lennie. Lennie was George's faithful companion. How could anyone think otherwise?
The ranch hands viewed Candy's dog as a nuisance. He had become absolutely useless. He served no purpose so the ranch hands felt he had to be shot.
In much the same way, George shoots Lennie because he had caused so much trouble. George did not want Lennie to suffer at Curley's hand so he shot Lennie to keep him from being tortured by Curley.
Steinbeck's message is that when you are all used up, someone takes you out back and shoots you. It is sad, but it is true. Candy's dog and Lennie had become troublesome and in the way.