In Letters to Menoeceus, what does Epicurus mean in claiming, "death ... is nothing to us," and how does he argue for it?
Epicurus' belief was that the world came into being, humanity included, through a chance collision of atoms and that at death the atoms comprising the body are released into the space again as nonsubstantial particles. Therefore death in a sense is a nonentity since no consciousness and nothing perceptive remains afterward, as all are dispersed in space.
It is this philosophical perception of the physics of death that renders death devoid of that which is terrible or fearsome. This is why Epicurus says, "So death, the most terrifying of ills, is nothing to us," in Letter to Menoeceus. Epicurus argues for his position through the proposition that soul-atoms dissipate into space from which they came via an accidental collision with no sentience retained within them.
Looking at it conversely, if consciousness remained, if the soul-atoms retained the form of substance though without substance (ghost or spirit), if death had some sentient capacity, then death would possess qualities that may provoke fear or a perception of terribleness. Without these qualities, then death is not present with the living and the living are nonexistent in death. Death is nothing to us.