If you recall, at this point in the story, Billy does not a coonskin with which to train his dogs to become coon hunters, so in order to get a skin, Billy has to set up traps, traps that are deemed cruel and unfair in Papa's opinion, and we see just how cruel the traps are for Papa
...whacked the coon a good one across the head, He let out a loud squall, growled, and showed his teeth. He tried to get Papa but the trap held him.
In this passage, the narrator reveals a image of Papa killing the coon that is trapped in one of Billy's traps, and it is a most cruel and unfair means by which Papa has to kill the coon. One the coon cannot escape which is unfair, and second Papa does not whack the coon once, he has to do it twice.
After the killing of the coon, the narrator tells us that
A sorrowful look came over Papa's face as he ran his fingers through the soft, yellow hair. "Billy," he said, "I want you to take a hammer and pull the nails from every one of those traps. It's summertime now and their fur isn't any good. Besides, I don't think this is very sportsmanlike. The coon doesn't have a chance. It's all right this time. You needed this one, but from now on I want you to catch them with your dogs. That way they have a fifty-fifty chance."
The passage clearly reveals Papa reasons for instructing Billy to dismantle his traps; the traps are unfair.