Carlson is selfish, and the only reason he does not like the dog is because it smells.
Carlson has no concept of what the dog means to Candy. He does not appreciate that Candy loves the dog, and the dog is his companion. The dog just annoys him because it smells.
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. (ch 2)
From Carlson’s point of view, one dog is just as good as another dog. He does not appreciate how much Candy loves the dog, so does not see why killing it and replacing it with a puppy is not just as good.
Carlson is annoying enough to get his way, and the dog is killed. Candy is devastated, but Carlson barely notices because he is completely selfish.
Carlson's special objection to the smell of Candy's old dog is an example of Steinbeck's use of indirect characterization (see the reference link below). To begin with, Carlson owns a German Luger which he apparently treasures. The gun will become important to the plot when George steals it to kill Lennie. Carlson is not young or old. He is one of the characters who, like Slim, appears to be middle-aged. Carlson apparently served in World War I approximatly twenty years ago and brought the Luger back as a souvenir. It reminds him of a time when he was young and full of courage and self-confidence, when he felt that he was a part of an important cause and had a purpose for living. He might have been a noncommissioned officer.
Now, however, he finds himself doing back-breaking farm work from morning to night just to maintain a mere existence. Along with a lot of other losers, he sleeps in a bunk on a mattress made of straw covered with burlap. He has his own private apple box nailed to the wall above his bunk for storing his few personal possessions.
Near one wall there was a black cast-iron stove, its stovepipe going straight up through the ceiling. In the middle of the room stood a big square table littered with playing cards, and around it were grouped boxes for the players to sit on.
There's no place like home!The men didn't even have chairs to sit on.
When George looks at his new bunk, he finds a yellow can that has a caption on the label reading:
"Positively kills lice, roaches and other scourges."
Carlson has to wash in a basin outside, and he probably has to use an outhouse. The food is not good and there is barely enough to go around. Candy tells George the former occupant of his bunk quit because he didn't like the food, and a little later on Slim says to George and Lennie:
"You guys better come on while they's still something to eat. Won't be nothing left in a couple of minutes."
Carlson objects to the pervasive smell of Candy's old dog because it reminds him of his past, present and future. When he was young he was full of the optimism and confidence of youth. Now he is middle-aged and finds himself living in miserable conditions and growing older every day without any hope for the future. The dog's smell is a constant reminder of his former dreams of glory, his present living and working situation, and his bleak, uncertain future when he may unable to maintain even the standard of living he enjoys now. The dog's smell is the smell of Carlson's life.
It is no wonder that Carlson seems surly, unsociable, dissatisfied, selfish, and somewhat cruel. There must have been plenty of men like him in the Depression Era, and Steinbeck must have run into a lot of them. The younger men did not share Carlson's pessimistic attitude because they had hopes that conditions would change and they could still realize their dreams. They could still get married and have children and homes of their own. Men like Carlson were caught at a bad time of life. Time was running out on them. George and Lennie appear to be still young enough to have plans and hopes for the future, but Carlson has nothing to look forward to but drudgery, loneliness, and squalor. He enjoys shooting Candy's dog. It gives him a chance to fire his precious Luger, and it gives him an opportunity to vent his anger at life.