Amy tan uses this description to show that she

1) wants to hide her true feelings about Robert.

Explanation:

In the story, Amy Tan is very much in love with Robert. That is why, when he and his family arrive for the Christmas dinner, she is trying hard to hide her feelings. She does this by ignoring Robert, and pretending she is better than him by acting as if he is "not worthy of existence".

This is the tactic of the opposite sometimes used by people when they like someone - they will act very disinterested in order to draw their attention and seem cool.