The conflict in Amy Tan's story "Two Kinds" revolves around Jing-mei's mother's attempts to make Jing-mei into a child prodigy. Early on in the process, Jing-mei starts to believe that her mother's efforts mean that her mother doesn't adore her. She promises she won't let her mother change her into something she's not.
Suyuan, Jing-mei's mother, believes that anyone can do anything in America and that Jing-mei could succeed at all these attempts at being a prodigy if she would only buckle down and put more effort into it. She arranges for her to take piano lessons, but Jing-mei doesn't put herself into playing piano. In fact, she embarrasses herself and her family by performing poorly at a recital. After that, Jing-mei refuses to practice the piano anymore. As she asserts her will against her mother, she feels "as if my true self had finally emerged."
Although her mother physically carries her to the piano bench and tries to force her to play, Jing-mei fights back, shouting, "You want me to be someone that I'm not!" This type of reaction does not move her mother; she only insists on obedience. But then Jing-mei brings up the babies that her mother had lost in China, "the ones we never talked about." She says that she would rather be dead like them than have to have Suyuan for her mother.
This outburst breaks Suyuan: "she backed out of the room, stunned, as if she were blowing away like a small brown leaf, thin, brittle, lifeless." After this Suyuan never demands that Jing-mei practice the piano again, and it is closed up. Was the conflict settled? Not exactly. Even years later, when the mother offered to give Jing-mei the piano as a present for her thirtieth birthday, she could not do so without saying, "You could been [sic] genius if you want to.... You just not trying." Although the mother and daughter have had a truce about her being a prodigy for almost two decades, the conflict was never really settled. The mother still believed Jing-mei was not trying, and Jing-mei still believed her mother wanted her to be someone else. Nevertheless, Jing-mei takes satisfaction from her mother's offering her the piano, viewing the piano "as if it were a shiny trophy [she] had won back."