Amy Tan and her mother share a complicated relationship, as is true of most mothers and daughters. The very title of "Two Kinds" hints at this and also at the final two pieces referenced in the end of this story.
On one hand, Tan is the "Pleading Child." She wants her mother to accept her with all of her shortcomings. She is weary of trying to live up to all of her mother's hopes and dreams. She wants to give up on becoming the genius that her mother believes her to be. But, after an outburst about the piano lessons, her mother wants her to continue. Tan is told:
Only two kinds of daughters. Those who are obedient and those who follow their own mind. Only one kind of daughter can live in this house. Obedient daughter!
Tan then hits her mother with a painful blow and tells her that she'd rather be dead—like the babies her mother lost.
On the other hand, she grows to be "Perfectly Contented" with what their relationship is. Tan won the argument and never had to take lessons again. And in retrospect she is disappointed because she feels like her mother gave up on her. She never asks her mother why she had set goals so high for Tan that failure seemed inevitable and never asks why she lost hope. However, Tan's mother actually gifts her with the piano for her thirtieth birthday and tells her, "You only one can play . . . You pick up fast . . . You could be a genius if you want to." After this, she views the piano differently, like a "shiny trophy" and notes, "It made me feel proud."
From her mother's point of view, she witnessed this "Pleading Child" floundering for goals and tried to help Tan find her strengths. However, she seems "Perfectly Contented" with the way her daughter emerges into her adulthood. She is proud of her, despite the fact that she never proved herself a genius.
In the last line, Tan writes, "I realized they were both halves of the same song." Her mother has passed away by the end, and Tan realizes that their experience was complex. They both struggled and they had found contentment with each other. The entire experience created their song, together.