Egwene knows Nynaeve. As much as detractors want to vilify her, she knew that Nynaeve could see her point if it was presented to her in precisely the way that Egwene did it. Elayne understands the importance of maintaining her public persona while having a personal identity because she was groomed for leadership, but Nynaeve had to grow into her position as a Wisdom and even now, has to mature some more before she's completely comfortable being an Aes Sedai. Rand, Mat and Perrin all struggle with this, as well.