There is no sense in defending yourself against people who are certain they are better than you are.
I believe this to be the thesis of the piece because the overarching theme seems to be Brown telling her daughter to hold her head high, no matter what criticisms are whispered around her. She states early on "I will teach you that the language of 'better than' is dangerous," and repeats the use of the phrase "better than" throughout the essay. It seems that all of her supporting claims include this language somewhere, or hark back to this statement. If I were to revise this thesis statement, I would try to include a supporting claim in the same sentence, as well as more precise language. "It is futile to defend your actions to those who would believe they are better than you, because not only does it exhaust you, but it will never change their opinions."