the death of Menelaus would be a disgrace for Agamemnon, not simply because others would charge him with failing to protect his brother, or because his death would give their enemies a chance to dishonour them both, but also because it would negate the whole purpose of his mission
Cairns argues that Menelaus functions as the linchpin of Agamemnon’s honor-system, such that his death would constitute a collective disgrace rooted in the structural failure of the Greek mission rather than mere personal loss.
, Aidos: The Psychology and Ethics of Honour and Shame in Ancient Greek Literature, 1993thesis