In "Two Kinds," what does the daughter realize when she becomes angry at her reflection in the mirror?

The episode with the mirror illustrates both Jing-Mei's increasing lack of self-worth and her sudden discovery of who she really is. Her mother, Suyuan, has been trying to turn her into some kind of child prodigy, subjecting her to constant testing. Suyuan believes that creating such a hothouse environment will help Jing-Mei become a genius.
But it doesn't work out like that. Jing-Mei cracks under the strain of her mother's demanding, unrealistic expectations. Not only does she struggle to achieve the hoped-for success (hoped-for by her mother, at any rate), she also starts to develop serious self-esteem issues. In failing to come up to scratch as a prodigy, Jing-Mei feels she's letting down her mother. In a fit of self-loathing, she looks at her reflection in the mirror and cries bitterly over what she sees as her "sad and ugly" expression. But then she has something of an epiphany, and self-loathing soon turns to defiance. It is then that she realizes she can never become what her mother wants her to be, and so she vows that she will not allow Suyuan to change her.