The central theme of "Two Kinds" is the conflict of expectations and culture between mother and daughter. "Two Kinds" is a section of the Joy Luck Club by Amy Tan that tells the story of June, her mother, and June's inability to play the piano well.
June struggles against her mother's expectations for two reasons: first, because they are mother and daughter; second, because they have different cultural backgrounds.
The struggle for power between generations of a family is a common theme in literature. In this case, it's represented by piano lessons. Suyuan, June's mother, dreams of her daughter being a famous piano player. For Suyuan, it's a way for June to grow beyond Suyuan's own career, house-cleaning. To June, however, the piano lessons are a way for her to fail her mother. The more disappointed Suyuan is in her progress, the more June resents both her mother and the piano lessons.
"Two Kinds" also shows the conflict of cultures between the two women. June is an American and Suyuan is Chinese. She moved from China believing in the American ideal that her daughter could be anything—and paired that with the Chinese belief that June should honor her and her wishes over June's own desires. June, on the other hand, doesn't have the same cultural values. She's more interested in becoming an empowered woman with her own desires.
After she fails at the talent show, June believes that Suyuan won't want her to continue the lessons. She's wrong. It sparks a fight where Suyuan explains that there are two kinds of daughters: the ones who are obedient and the ones who do what they want. June attacks her with the painful memory of the twin Suyuan left for dead in China. June is able to stop the piano lessons and reflects in adulthood that it created a schism between her and Suyuan.