This story is not just about animal cruelty, although it is clearly about that. Rather, it is about the way humans influence each other. Something about Palmer makes him see peer pressure when it happens, and he always feels most influenced by those he spends time with. The animal cruelty is the symbol for a kind of injustice that Palmer sees, but no one else does. He feels that it would be wrong to harm any living being, but his community says to him to do it anyway.
That sets him up for a serious ethical dilemma. Perhaps he is wrong. After all, everyone else seems to agree with the status quo. Even his own father is complicit in the hunt—not just complicit, but also an active participant. He is known for killing many, many birds on "Family Fest" day. With a moral example like that, he begins to question is own judgment.
Ultimately, he works through this by noticing a slight change in his treasured friendship with Dorothy. The pressure he feels to be like his friends (who bully him) shapes him into a broken, emotionally fragile person that mistreats Dorothy. He is smart enough to notice that happening, and he draws the conclusion that this is actually an instance where he should stick to his guns by not killing anything ever.
