"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.