How do the crab and the cat serve as metaphors for June's understanding of herself and her relationship with her mother in Two Kinds?
This question refers to the chapter "Best Quality," in which Jing-Mei, or June, remembers the last New Year's dinner her mother cooked when she prepared crab for her friends. Jing-Mei thinks she is doing the right thing when she takes the smallest crab, but is surprised when her mother insists that she takes the larger one. After the dinner, her mother says to her:
Only you pick that crab. Nobody else take it. I already know this. Everybody else want best quality. You thinking different.
Even though Jing-Mei interprets this as being "proof of something good," it is perhaps more likely that Jing-Mei's mother is trying to get her daughter to realise she deserves better than constantly settling for second best. By taking the smaller crab that is actually no good for eating, Jing-Mei's actions show this aspect of her character.
In the same way, the cat acts as a symbol of the relationship between Jing-Mei and her mother. Jing-Mei's mother tries to get rid of the cat in her life, seeing it as a pest to be gotten rid of. However, Jing-Mei is relieved to see that the cat returns after her mother's death, even though it hisses at her. The cat symbolises her mother's presence and her expectations of her daughter. Even though she is dead, Jing-Mei's mother still wants her daughter to realise she deserves better than she currently settles for, and this truth is an annoying presence represented in the form of the cat.