The author's purpose is to share several important messages with us. One is about youth and age. The young can never imagine that the old were once just as they are now; they feel they will always be young and strong and therefore they sometimes lack compassion for the old.
Another theme is the way we hate what we are, often. The old woman, her poverty and degradation, remind the narrator too vividly of their shared plight. Secretly, then, perhaps the narrator DOES indeed understand her possible fate. She cannot bear to see what she might become so she tries to destroy it.
The author also wants us to understand that beauty can blossom anywhere. The old woman's love of her garden symbolizes the human spirit, fiery and unquenchable. Sadly, that flame seems to be permanently extinguished by the girl's actions. "Despite my wild contrition" is a phrase from the story that always sticks with me. Sometimes we cannot take back our actions or words, no matter how contrite we are.