In the story "Two Kinds" by Amy Tan, why does the piano symbolize a trophy in the end?

In the end, the piano is depicted as a trophy because it represents sacrifice, hard work, initiative, and investment, all the components needed for success in any field. Jing-mei's parents saved to purchase a black, Wurlitzer second-hand piano because they believed that the piano would lead to a great future for Jing-mei. Equally proud of the instrument, Jing-mei tells us that the piano was the "showpiece" of their living-room. More than anything, the piano represents the complexities of a mother's love.
The piano is at once an object of conflict as well as an object of a mother's faith. While Jing-mei is initially buoyed by her mother's belief in her abilities, she comes to dread her mother's smothering presence in her life. As the days progress, Jing-mei begins to feel as if she's on a constant, wearying mission to discover her prodigy potential. Home becomes a battlefield, and music becomes a topic fraught with stress and frustration.
In the end, to thwart what she considers her mother's foolish expectations, Jing-mei decides to teach her a lesson; she embarrasses her parents at a piano recital by playing poorly. In the end, after an especially emotional confrontation with her mother, Jing-mei is allowed to leave off playing the piano. The instrument sits unused in her parents' living room until Jing-mei's mother offers her the piano for her thirtieth birthday. Her mother's words remind Jing-mei that she has always been loved:

"Always your piano. You only one can play..."You pick up fast," my mother said, as if she knew this was certain. “You have natural talent. You could be a genius if you want to." "No, I couldn't." "You just not trying," my mother said. And she was neither angry nor sad. She said it as if announcing a fact that could never be disproved.

On the one hand, Jing-mei's mother has always believed in Jing-mei's potential to excel. On the other hand, her high expectations for Jing-mei created strife in their relationship during Jing-mei's childhood years. Perhaps, after so many years, Jing-mei's mother realizes the part she unwittingly played in her daughter's failure, for her matter-of-fact tone as she gives Jing-mei the piano betrays the secrets of her inner heart. So, in her adult years, Jing-mei comes to see the piano as a trophy, an emblem of a mother's love, faith, and acceptance, all the things she had always needed from her mother.