In the beginning of the story, Jing-mei is excited about being a prodigy. However, when she does not seem to have a special talent she gets frustrated. She does not want her mother to push her into anything.
Jing-mei might have been more open to the idea of being a prodigy if her mother had asked for input from her on what talents to try. Her mother seems to just come up with a lot of random talents from stories of prodigies in magazines.
The tests got harder - multiplying numbers in my head, finding the queen of hearts in a deck of cards, trying to stand on my head without using my hands, predicting the daily temperatures in Los angeles, New York, and London.
Jing-mei soon loses patience with her mother. Jing-mei looks back at her reflection and realizes she is not the person she was. Her mother is trying to change her.
The girl staring back at me was angry, powerful. She and I were the same. I had new thoughts, willful thoughts - or rather, thoughts filled with lots of won'ts. I won't let her change me, I promised myself. I won't be what I'm not.
This is when Jing-mei gives up on the prodigy idea. She tells herself that she is not going to try to learn the piano, because it is not who she is. She is no longer willing to play along.
You can train someone, but you cannot make a person a prodigy.