The ongoing three-way public-relations car wreck involving Washington, Facebook, and Sheryl Sandberg, the company’s powerful C.O.O., begs a question of America’s esteemed managerial class. How has someone with such sterling Establishment credentials—Harvard University, Harvard Business School, the Clinton administration—managed to find herself in such a pickle? The answer won’t be found in the minutes of Facebook board meetings or in Sandberg’s best-selling books, Lean In and Option B, which cemented her position in the corporate firmament as a feminist heroine.