Egwene, Nynaeve and Elayne continue to masquerade as full Aes Sedai; interrogating the two captured Black Ajah Sisters. Moiraine seems to have delegated this task to the three women, for purposes she keeps to herself. Despite the importance of their task - drawing forth intelligence to piece together the Black Ajah's plan - Egwene and Nynaeve still continue their squabble.
Elayne usually smoothed things over when it came to this, as it did more often than it should. By the time Egwene thought of smoothing matters herself, she had almost always dug in her heels and flared back, and trying to be soothing then would only be backing down. That was how Nynaeve would see it, she was sure. She could not remember Nynaeve ever making any move to back down, so why should she? This time Elayne was not there; Moiraine had summoned the Daughter-Heir with a word and a gesture to follow the Maiden who had come for the Aes Sedai. Without her, the tension stretched, each of the Accepted waiting for the other to blink first. Aviendha barely breathed; she kept herself strictly out of their confrontations. No doubt she considered it simple wisdom to stand clear.
Egwene, The Shadow Rising, p. 83
This little spat is still going strong. Egwene blames Nynaeve for her response, to justify her own similar response. The two are falling victim to the idea that backing down means giving up completely. Not at all the case; Egwene could back down from the current position to maneuver around to a more suitable one and re-engage. Since each is holding so tightly to their current position, they are left open to other arguments from other angles.
Or, simpler still, Egwene just needs to put her hat in her hands (so to speak) and make the offer to come to an agreement. It's much harder - admitting wrongdoing, asking for help - all seem to imply a position of weakness. Not at all true. Most people, once asked, will spend a great deal of effort in teaching whatever skill is needed. This happened to me in my shipyard days. Part of my job was to qualify in a particular position; it wasn't an overly challenging qualification, it was simply uninteresting to me. And I had had some less than positive interactions with the lead qualifier. So I procrastinated. Until I was left with mere weeks to complete it. I went to the lead qualifier and simply asked for his help. To my utter surprise, he bent over backwards to help; starting that very minute. I had let something fester that I had no need to; simply out of my own stubbornness. As it turns out, he became one of my biggest advocates in obtaining that qualification - so I really was my own worst enemy. All I had to do was just ask.