Why did Waverly tell her mother, "I wish you wouldn't do that, telling everybody I'm your daughter"?

Waverly feels like her mother is living through her achievements.

Although she makes a point to explain that a Chinese woman is careful about showing pride, Waverly feels that her mother takes too much credit for Waverly’s accomplishments.  Although her mother doesn’t come out and admit that she admires her daughter, she basks in her glow.

When Waverly’s family first gets a chess set, her mom is not interested in it.  Then Waverly turns out to be very good, and her mother takes notice.  She is proud of her daughter’s success and properly lets everyone know it

A small weekend crowd of Chinese people and tourists would gather as I played and defeated my opponents one by one. My mother would join the crowds during these outdoor exhibition games. She sat proudly on the bench, telling my admirers with proper Chinese humility, "Is luck."

As she won more and more games, Waverly gained enough attention to be on magazine covers.  Her wins were celebrated in local stores.  Waverly’s mother basked in her daughter’s glory, and Waverly just got tired of it.

"Aii-ya. So shame be with mother?" She grasped my hand even tighter as she glared at me.

I looked down. "It's not that, it's just so obvious. It's just so embarrassing."

"Embarrass you be my daughter?" Her voice was cracking with anger. "That's not what I meant. That's not what I said."

After Waverly and her mother have this fight, Waverly runs off.  She doesn’t know what to do.  When Waverly tells her mother to stop showing her off, her mother feels terrible.  She feels like her daughter is ashamed of her. 

Waverly realizes that her words hurt her mother.  She didn't mean to hurt her, but she wants chess to be her thing. Her mother tries to hide her feelings by saying that the family should not talk to Waverly.  Waverly is not sure how things will be for them from then on.