A parent’s love can be described as a double-edged sword, as it has the power to both defend and destroy a child. Explain how this is true in the case of Waverly’s mother.

A parent’s love certainly has the power to both defend and destroy a child.
In the story, the mother clearly loves her daughter. Daily, she shares tidbits of generational wisdom with her daughter. Waverly tells us that her mother is always focused on the future.

My mother imparted her daily truths, so she could help my older brothers and me rise above our circumstances.

To Waverly's mother, success is not dependent on luck. As such, wisdom must be cultivated and used as a tool to engineer one's success in life.
When Waverly's brother receives a used chess set for Christmas, Waverly becomes curious about this foreign Western game. She inquires about its rules, but Vincent (her brother) has little patience for her inquisitive questions.
Waverley's mother encourages her to learn the rules for herself. This is how Waverly comes to excel at chess.

I learned about opening moves and why it's important to control the center early on . . . I learned about the middle game and why tactics between two adversaries are like clashing ideas; the one who plays better has the clearest plans for both attacking and getting out of traps. I learned why it is essential in the endgame to have foresight, a mathematical understanding of all possible moves, and patience; all weaknesses and advantages become evident to a strong adversary and are obscured to a tiring opponent. I discovered that for the whole game one must gather invisible strengths and see the endgame before the game begins.

Seeing her natural propensity for the game, Waverly's mother supports her as she gains new skills. She even defends Waverly when her brothers complain about having to do their sister's chores.

"Is new American rules," said my mother. "Meimei play, squeeze all her brains out for win chess. You play, worth squeeze towel."

By her ninth birthday, Waverly is a national chess champion. Her mother is justifiably proud of her, but a new conflict soon arises. For her part, Waverly resents being used as a means for her mother to "show off." She feels pressured to perform in order to keep her mother's approval. Before she knows it, Waverly begins to apply her recently acquired chess skills to life. She leverages the strategies she has carefully honed to prevail in a power struggle against her mother. This sets up a bitter rivalry between the two.
Even though Waverly's mother initially acts out of love, her obsession with status and success destroys the positive feelings between her and her daughter. Waverly comes to resent the pressure put upon her to excel. She no longer sees her mother's efforts on her behalf as loving actions. Instead of focusing on improving her chess skills and, thus, her prospects for the future, Waverly becomes preoccupied with retaliatory thoughts against her mother. In this way, a mother's love has the power to both defend and destroy her child.