In Chapter 18, Athena appears before Circe and demands that she surrender Telegonus to be killed. Athena uses logos and pathos to try to persuade Circe that it is better to give him up now rather than later:
"[D]o not let a mother’s doting cloud your sense. Think, daughter of Helios. Is it not wiser to give him to me now, when he is barely set into the world, when his flesh and your affections are still half formed?” Her voice softened. “Imagine how much worse it will be for you in a year, or two, or ten, when your love is full-grown. Better to send him easy to the house of souls now. Better to bear another child and begin to forget with new joys."
Athena implores Circe to "think" and use her "sense" instead of her emotions. And yet, she does not present a reason why Telegonus must die other than that she says it must be so. This reason is not good enough to override Circe's maternal devotion. To convince Circe to stop protecting her child, Athena finds that she has no choice but to bring emotion into her argument. She does so clumsily. First, she asks Circe to imagine the grief she would feel to surrender her son years from now, when their bond is even stronger. Then, she suggests that Circe could trade this all-consuming grief for joy simply by letting Telegonus go and having a substitute child. Athena thus sets up a false binary between grief and joy as the two choices Circe can choose between.
As the goddess of wisdom, Athena is supposed to have impeccable logic and argumentation. In this scene, however, her argument falls apart. She clearly does not understand the bond between Circe and her son. It may be impossibly difficult for Circe to let Telegonus die once he is older, but that does not mean that it will be any less difficult now. A child does not need to be "full-grown" for their parent to love them fully. The idea that Circe might forget Telegonus if she were to have another child is both laughable and insulting to her. Athena's unskilled use of pathos thus undermines her logos. No matter what she believes about the superiority of "sense" as a basis for decisions, she would be a better debater were she to gain a better understanding of emotion.
Furthermore, it is worth noting that Athena refuses to tell Circe why she wants to kill Telegonus at all. As it turns out, it is because he is fated to kill Odysseus, Athena's pet mortal. Athena can't stand the idea that Odysseus will die so tragically. Were she to admit her fear to Circe, Circe would surely still protect her son. However, the two goddesses might have had a more productive discussion about their values and may even have found a way to protect both men. Athena's argument thus falls apart not only because she fails to understand and appeal to Circe's emotions, but also because she refuses to admit to her own.