The two main characters in "Two Kinds" are Jing-mei, and her mother, Suyuan. Suyuan wants her daughter to be a prodigy and pushes her from a young age to perform. Her reasons for having such high expectations for her daughter include feeling competitive with her friend Lindo and wanting the best life possible for her daughter. Lindo's daughter, Waverly, is a true prodigy, having become a national chess champion at only nine years of age. Suyuan has to put up with Lindo's flaunting of Waverly's talents, and she would like to be able to have something with which to counter those boasts. Still, she tells Jing-mei, and it is certainly partially true, that she wants her to excel "for you [sic] sake." She wants her child to take advantage of all the opportunity America offers, especially since she came from China, where options were much more limited. Another subconscious motivation for Suyuan in having Jing-mei succeed is to make up for Suyuan's two baby girls whom she lost in China. In a sense, Suyuan needs Jing-mei to live three lives in one since those two baby girls never got to grow up with their mother.
Jing-mei at first is motivated by wanting to please her mother. She buys into the efforts to become a prodigy, thinking that when she did, "my mother and father would adore me. I would be beyond reproach." This motivation is short-lived. When she realizes she is not prodigy material, she has a meeting with herself in front of the mirror and decides, "I won't be what I'm not." Now her motivation is to be herself, not what someone else wants her to be. This motivation continues to grow as Jing-mei behaves first with passive defiance and then with outright rebellion towards her mother. Her desire is to be herself and to be loved for who she is, not for what someone can make of her.
These motivations are in obvious conflict--a conflict that cannot be resolved peacefully because the mother and daughter can't seem to communicate effectively with each other.