One of June's character traits in Tan's "Two Kinds" is that she is fundamentally trapped. June is trapped between the world of her Chinese ancestry and the American world around her. This character trait underscores her narrative in the story. She feels the need to appease her mother's wishes, but at the same time actively resents it and rebels against it. June feels trapped between both worlds because she is unable to find happiness in either one. She recognizes that she will never be the piano prodigy her mother wishes. This trait of being trapped is evident in the exchange between mother and daughter about playing the piano:
"Why don't you like me the way I am?" I cried. "I'm not a genius! I can't play the piano. And even if I could, I wouldn't go on TV if you paid me a million dollars!"
My mother slapped me. "Who ask you to be genius?" she shouted. "Only ask you be your best. For you sake. You think I want you to be genius? Hnnh! What for! Who ask you!”?
June clearly understands that she will not find happiness in outwardly rejecting her mother's wishes. She lives at the hyphen of being "Asian- American," and is trapped between both worlds, unable to find happiness in either.
Another character trait that June shows is a sobering self- awareness. June clearly recognizes her own limitations. Her mother does not see this as much as June does. June understands that she is "not a genius." She demonstrates this trait when she is playing the piano for her auditory limited teacher: "I would play after him, the simple scale, the simple chord, and then just play some nonsense that sounded like a cat running up and down on top of garbage cans." The "simple" extent to which June would play the piano clearly demonstrates that June understands her own condition and accepts the limitations of her own place in the world: "Unlike my mother, I did not believe I could be anything I wanted to be, I could only be me." This represents part of the fundamental collision between June and her mother.
Finally, the ending of the story displays June as one who seeks to bring unity to that which has been fragmented. June's trait of wishing for harmony is not simply literal in how she wishes the piano to be tuned, honoring her mother's wishes. Rather, she wishes to appease her mother, even after death. In recognizing that the melodies she plays are "two halves of the same song," June has displayed a desire to reconcile that which was previously separate and no longer living at the hyphen of being in the world.