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.

A central theme in Amy Tan's story is the inevitability of conflict between what our parents want for us and what we want for ourselves. As a young girl, the narrator and her mother agreed that fame and success were highly desirable and quite possibly within her reach. But trial and error and encountering the realization that to excel means total dedication and unrelenting practice led the narrator to understand that she was not being allowed to truly be herself and follow her own genuine interests. The rebelliousness of her teen years solidified in their relationship, and it took many years for the narrator and her mother to offer forgiveness to each other. Ultimately, the daughter needed to take her own path in life, and her mother had to relinquish her own ideas. The piano, the symbol of the breaking point of the narrator's relationship with her mother, finally becomes a treasured possession, a relic of her childhood, but one without negative feelings associated with it. The mother giving the piano to her daughter, and the daughter reconditioning it and playing it for pleasure, represents a resolution of their conflict.

In "Two Kinds," Amy Tan examines the longing to achieve the American dream and the volatility of mother-daughter relationships. Jing-Mei’s mother yearns for her daughter to live the American dream, even if it is on the mother’s terms. Having lived through unimaginable horrors in her homeland of China, she sees countless opportunities for her daughter. Unfortunately, the mother’s authoritarian tactics eventually drive her daughter away and develop a rift between mother and daughter.

Jing-Mei rebels and attempts to live life on her own terms. She never achieves her mother’s vision of the American dream, but she does create her own life with its trials and tribulations. It is not until after her mother’s death that she realizes it took both her mother’s fortitude and her own initiative to create a full life.

The central idea of “Two Kinds” is Jing-Mei’s journey to discover her identity in spite of her mother’s demands for an obedient daughter who was focused on an idealized image of American prosperity.

The narrator refers to "the prodigy in [her]" as a child when she imagined all the possibilities for her fame-filled, glorious future, possibilities fed by her mother's urging and insistence.  This prodigy becomes a metaphor for the narrator's inner feelings.  However, the more her mother tested her, the more she failed: naming capitals, doing multiplication tables, saying everything she remembered from a page in the Bible, and so on.  She began to feel that "something inside [her] began to die" because of all the disappointment she so clearly saw on her mother's face.

Soon, she looks in the mirror and feels as though she can see the prodigy's reflection, and "The girl staring back at [her] was angry, powerful. . . . [She] had new thoughts, willful thoughts—or rather, thoughts filled with lots of won'ts."  It is not a prodigy inside her; rather, the prodigy is a metaphor for her feelings of rebellion.  She learned to fight back against her mother, to be disobedient, and do what she wanted, instead of what her mother told her to do.  As the years pass, this rebel "assert[s] [her] will, [her] right to fall short of expectations."  Even though she might have been a pretty good piano player, it was more important to not try, "not to be anybody different."  It turns out, then, that she really is a prodigy, a prodigy of rebellion!  She practices and practices, and eventually wins the trophy of the piano, a testament to her powerful will.

Let us remind ourselves that a metaphor is a piece of figurative language that compares one object to something else by asserting a direct comparison, without using the words "like" or "as." The most important metaphor in this story about the conflict between a mother and her daughter actually comes towards the end of the text, when Jing-Mei's mother gives the piano to her daughter in spite of the many disappointments she has caused her mother. Having asserted her "right" to "fall short of expectations," Jing-Mei sees this gift as a sign of acceptance of who she is and who she has become from a mother who has always appeared to want her to be more than she is. Note how the piano is described:

And after that, every time I saw it in my parents' living room, standign in front of the bay windows, it made me feel proud, as if it were a shiny trophy I had won back.

Now how the piano is described as a "shiny trophy." Jing-Mei obviously feels that she can use this metaphor to describe the piano this way because she believes she has won this trophy on her own terms and has not conformed to her mother's crippling expectations for her.

Intergenerational conflict has long been a fruitful theme for writers to explore. But it’s especially fruitful when such conflict is exacerbated by cultural differences between one generation and the next. This often happens in immigrant families, where the parents are often separated from their children by a vast cultural chasm. Differences in host language proficiency and degrees of cultural assimilation all too often lead to a breakdown in communications between one generation and the next.

This is what appears to have happened in “Two Kinds” by Amy Tan. Jing-mei, having been born and raised in the United States, feels herself to be more American than Chinese. Her mother, on the other hand, who was born in China and spent her early life there, still adheres to the old traditions, such as insisting on the absolute obedience of her children.

Inevitably, this generates considerable tension between herself and her daughter. Jing-mei is a very independent young person and doesn’t take kindly to her mother bossing her around and trying to mold her into a child prodigy against her will. For her part, Jing-mei’s mother is insistent that there are only two kinds of daughters: “those who are obedient and those who follow their own mind!” Jing-mei’s mother firmly expects her daughter to fall into the first category.

Your thesis could explore any number of pieces of "Two Kinds." There isn't only a single correct thesis that can or should be written about the story. One thing to keep in mind is that a thesis statement makes an argument. Your thesis statement needs to make an argument about some part of Tan's story. Your argument could be about a character, theme, or some other literary aspect, like setting or point of view. My recommendation would be to explore a theme and use Jing Mei and Suyuan to explore that theme. You could explore themes of family, tradition, cultural identification, rebellion, or forgiveness.

Once you decide on a thesis direction, your next goal is to craft the actual thesis. Thesis writing is tough. You want the thesis to make an argument. You also want it to be specific; however, you want a thesis to be broad enough to give you enough latitude to explore the entire text. This means that a thesis that states two sides of an argument can work quite well because it allows you to explore your argument as well as the counterargument. For example, the following thesis might work well for "Two Kinds." Although Jing Mei's attitude may seem like typical teenage rebellion, her actions more clearly illustrate a teenager's desire to be accepted for who they are."

Amy Tan’s story “Two Kinds” has several levels of content.  Primarily, it is a struggle between a mother and daughter.  The mother believes that in America a person can be anything that he wants to be.  Furthermore, she believes that her daughter has many talents that she could utilize. 

The story is told from a flashback point of view.  The daughter is grown, and her parents have passed away.  When she looks back, Jing-Mei can see that her mother wants her to have a chance at life and to do the best that she can do.  Her mother decides that she could be a piano prodigy; arranging for lessons with a man in their apartment building, the mother cleans his apartment to pay for the lessons.

Fighting against her mother’s authority, Jing-Mei discovers that her teacher cannot hear; therefore, she wastes time during the lessons and pretends to practice.  When she fails to do well during a talent show, her mother is humiliated but does not intend to give in to her daughter.  However, her daughter refuses to continue the lessons. The mother‘s response gives the story its name:

“Only two kinds of daughters,” she shouted in Chinese. “Those who are obedient and those who follow their own mind! Only one kind of daughter can live in this house.  Obedient daughter!”

Jing-Mei wins the day but hurts her mother.  She yells back at her mother:

“Then I wish I wasn’t your daughter. I wish you weren’t my mother.”  I could sense my mother’s anger.  Then I remembered the babies that my mother lost in China.  “Then I wish I’d never been born!” she shouted.  “I wish I were dead! Like them!”

No mention is ever made again of the piano lessons. Jing-Mei struggles with her mother until she goes to college and realizes that she gave her mother many heartaches. 

In addition, there are other twos that could be discussed and directly impact the title of the story.  The mother who comes from China and is the first generation in this country butts heads with her daughter who was born in America and does not understand the Chinese way of thinking.  Despite her bearing down on her daughter, the mother becomes a sympathetic character who wants only the best for her daughter.

At the end of the story, Jing-Mei becomes the obedient daughter that her mother wanted when she sits down to play the piano.  She plays the two pieces that were intended for the talent show: “Pleading Child” and “Perfectly Contented.”  Then she realizes that they are two halves of the same song.  The songs become a metaphor suggesting that she is both kinds of the daughters. 

In “Two Kinds” by Amy Tan, the mother believes that a person can become whatever she chooses in America. Jing-Mei and her mother’s relationship are often difficult.  The mother expects more from her daughter than she is willing to give.

The setting for the story is in the protagonist’s home in Chinatown during the 1950s and 1960s.  The protagonist and narrator is the author herself: Amy Tan. Her mother is the antagonist of the story since she constantly expects her daughter to show some hidden talent and become a star. 

As a small child, the narrator’s mother wanted her child to show some kind of special talent.  After listening to her mother brag about other prodigies, Jing-Mei tires of it and decides to get back at her mother. Her mother makes a trade with Mr. Chong, a retired piano teacher, to give Jing-Mei lessons and the mother will clean his apartment.

 Jing-Mei learns quickly that the old teacher cannot hear.  She spends most of her lessons playing the wrong notes.  When it is recital time, the author embarrasses her family and herself by a humiliating performance of wrong notes.

The mother did not intend to give up on the lessons until the final confrontation between them. The narrator refuses to practice, and the mother grabs her.

‘You want me to be someone that I’m not! I’ll never am the kind of daughter you want me to be!’

'Only two kinds of daughter,' she shouted in Chinese.  ‘Those are obedient and those who follow their own mind!’

 Then, Jing-Mei says of the worst thing that she can think of.  She tells her mother that she wishes that she were dead like all of the babies that her mother left in China. Her mother never mentions the piano again. 

Finally, when Jing-Mei is thirty years old, the mother gives her the piano.  She does not do anything about it until after her mother passes away, and she is putting up her mother’s  things.

It is only after her mother's death that Jing-Mei begins to realize what her mother had wanted for her.  This realization brings together the lesson of the story which speaks the tension a parent and child.  The mother and daughter are separated by many factors — age, experience, ambition, and culture. To Jing-Mei’s mother, America is the Land of Opportunity. Her daughter could be anything that she wanted to be.

The narrator looks back over the music that she formerly shunned and discovers something that she had not noticed before. The song on the left-hand side ofthe page is called "Pleading Child"; the one on the right, "Perfectly Contented." Suddenly, Jing-Mei realizes that the two titles are two halves of the same song.  Like the song, Jing-Mei is two halves of the same person: American and Chinese and obedient and independent.

This is the theme of the story.  Her parents were immigrants to America.  Jing-Mei was born in America. She is unsure who she really is.  She struggles with her mother on the outside, but internally, Jing-Mei is uncertain as to whom she is

"Two Kinds" focuses on the mother/daughter dynamic.  Because Jing Mei's mother lived an extremely difficult life in China, she pressures Jing Mei to excel in America where it is much easier for a girl to be successful.  The problem is that Jing Mei's mother defines success for her daughter as being exceptional at something.  Thus, Jing Mei must take piano lessons in order to become a child protegee.

The title refers to Jing Mei's mother's statement that there are two kinds of daughters in the world--those who obey, and those who rebel.  For Jing Mei, as an adult, she can see a little bit of both in herself and is mature enough now to see what her mother was trying to do for her.

This short story above all else explores the relationship of Jing-Mei with her mother and the conflict that she experienced in her childhood as part of her journey towards womanhood and becoming confident in her own identity. The memories of Jing-Mei being constantly pushed towards excellence and being set hopelessly high expectations shows the arena of the conflict that she experienced with her mother. This is of course shown best through the piano debacle, when Jing-Mei delivers her shocking performance in front of everybody and therefore asserts her own will and makes her decision to be her own person rather than the person her mother would have her be. Note how she portrays this decision:

In the years that followed, I failed her so many times, each time asserting my own will, my right to fall short of expectations. I didn't get straight As. I didn't become class president. I didn't get into Stanford. I dropped out of college.

Jing-Mei supports this by saying that this "failure" resulted from her recognition that she could "only be" herself and could not be anything she wanted to be. The story ends with Jing-Mei's realisation that the song she played for her disastrous recital, "Pleading Child," was part of two pieces, the second entitled "Perfectly Contented." This implies that in the conflict she experienced with her mother is part of her journey of becoming a whole, strong and confident woman, and is inextricably linked with her identity now as an adult, where she has accepted herself and forged her own identity. The fact that these two pieces were "two halves of the same song" shows Jing-Mei's own acceptance of the journey she has taken to arrive at where she is now.

Amy Tan's story is primarily about coming of age. The main theme is learning about one's own identity. June tries many different activities and keeps taking piano lessons. However, she has her doubts about both her talent as a musician and the qualifications of her teacher, who is hard of hearing. As a child, her ability to chart her own course is highly constrained. Through her emotional outburst to her mother, she shows her unhappiness. June takes a large step in maturing when she admits that piano is not for her.

As much of the story deals with a mother-daughter relationship, another important theme is that parents need to give their children space to learn their own talents. June's mother cannot make all her decisions for her.

Please see the link below for another answer.

Like much of Tan's work in what came to be called "The Joy Luck Club," the theme of the story revolves around the challenges in the relationship between mother and daughter, past and present culture, and personal voice and social acceptance.  In their own way, each challenge is seen as "two kinds" of summits that individuals must climb in order to find some level of happiness in their lives.  The background involves a Chinese mother who believes in the authenticity of the American dream for her first generation Chinese American daughter.  The mother believes that the freedom offered in America can automatically translate into public success and demonstrative paths which highlight the fulfillment of "the American Dream."  In some respects, one can understand this because the mother's connection to her past is severed, as China has undergone the Cultural Revolution of Mao at the time, and the mother's arrival into America represents a moment where she has only the visions of America and its dreams to accompany her in her sojourn throughout her life.  The daughter, in contrast, is not burdened with such a past as she is an American citizen.  Her challenge, though, comes with being forced to embrace something that is not hers to embrace.  The mother accepts and strives to live the American Dream through her daughter, precisely because such opportunity was nonexistent for her in China.  This plays a formative role in how the mother interacts with her daughter.  The daughter wishes nothing more than "to be me."  Such a disparity and how it impacts mother- daughter relationships represent the theme of Tan's work.

Concerning Amy Tan's "Two Kinds," the enotes Study Guide on the story lists two themes.  I'll cite the two it mentions and explain them.

• The American Dream:  Immigrants are often influenced by the American Dream, and in this story the mother, obviously unable to attain it herself, possesses an all-encompassing desire to make her daughter do so.  Her unrealistic expectations ruin the relationship between her daughter and herself.
• Identity:  The mother sees herself always as a Chinese wife and mother.  She attempts to force her daughter into the mold she has in mind for her.  The daughter struggles with finding her own identity, and rejects the mold her mother wants to force her into. 

The mother attempts to live vicariously through her daughter, and force her into an unrealistic mold.  The daughter, unable to meet her mother's unrealistic expectations, rebels.

• Theme of Mother/Daughter Relationship

It is only after her mother's death that Jing-mei notices in the songbook for her piano that one side has the song "Pleading Child" while the other side has a song entitled, "Perfectly Contented." About two aspects of the same child, these songs demonstrate the theme of conflicts between mothers and daughters. While the mothers were born in China and have the old country's beliefs and ways, the daughters are American-born and, thus, do not understand the old culture.

Because her mother believes Jing-mei should excel in something, she has decided that her daughter will learn to play the piano and contracts with old Mr. Chong a deaf retired piano teacher. Besides being deaf, Mr. Chong has poor eyesight, so he cannot even tell if Jing-mei is playing the correct keys. Consequently, the child does not worry about practicing. Then, hearing her mother's declarations that she will be a prodigy, the daughter begins to believe she can be one without working. Sadly, at a recital, Jing-mei plays poorly and embarrasses her mother before friends and relatives. After this fiasco, Jing-mei assumes that her mother will let her stop her piano lessons. But, when she asks why she cannot quit, she receives this answer, 

"Only two kinds of daughters," she shouted in Chinese. "Those who are obedient and those who follow their own mind! Only one kind of daughter can live in this house. Obedient daughter!"

"Then I wish I'd never been born!" I shouted. “I wish I were dead! Like them." It was as if I had said magic words. Alakazam!-her face went blank, her mouth closed.

This ended the playing of the piano. But, when she turned thirty, her mother offered Jing-mei the piano as an act of forgiveness. After her mother dies, Jing-mei opens the two-part song and plays the piano again in understanding.