As with any piece of literature, the significance of the quote comes from it supporting your argument. If you wanted to talk about the way that animals and the seasons are treated by the narrator, the following quote could be useful:
He was a beautiful buck, the color of late-turned maple leaves.
This sentence makes an allusion to autumnal leaves, despite the story being set during winter. The buck's color being described this way is significant because it reinforces the naturalistic perspective that Andy has. This story is about a young girl's "loss of innocence" and part of that is that she is noticing the significance of natural beauty. There are also references to the seasons throughout the story, and how they affect the woods. These allude to the passage of time and the circle of life: Andy is maturing and moving from one "season" of her life into the next.
Another significant quote is about Andy's visit to the ocean. She makes a trip with her parents, and they go to the beach. Andy is hesitant to go into the ocean because she has not grown up going to the beach. Her mother is floating away from the shore and beckoning to Andy to come into the water.
That was the first time she'd seen the ocean, and it frightened her. It was huge and empty, yet always moving. Everything lay hidden. If you walked in it, you couldn't see how deep it was or what might be below; if you swam, something could pull you under and you'd never be seen again. Its musky, rank smell made her think of things dying.
This quote alludes to the depths of the ocean being scary and dark. The fear that Andy has of the ocean is a fear of the unknown, especially the unknown "depths" that exists in other people. The ocean is often used in literature as a metaphor for the subconscious mind; in this case, the ocean seems to be a metaphor for the subconscious mind
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