In Homer's The Odyssey, why is Ithaca still in danger after the suitors' deaths?
After Odysseus kills all the suitors who have been trying to get his wife to marry one of them, Ithaca is still in danger because a civil war could break out. Odysseus has come home and has killed all of these prominent men from the community, some in very horrible ways. Of course, this could well cause a great deal of anger among the families of the slain men.
This is what actually does happen in Book 24. Many of the suitors' family members march against Odysseus, planning to kill him and his allies. It is only the intervention of the gods that allows this to end relatively peacefully.
So Ithaca is still in danger exactly because Odysseus has slain the suitors, thus angering their families and making civil war a possibility.
Ithaca is in danger after the suitors' deaths precisely because of the suitors' deaths. Word gets around quickly that Odysseus has brutally slain the suitors, who, in many cases, were the most eligible young men of their families, and the families come to claim the bodies of their sons in order to give them proper burial. Some of the suitors had even come from other towns, and their bodies have to be sent home with the fishermen. Antinous's father, Eupeithes, is especially angry and speaks to the suitors' families to incite them to march on Odysseus and exact revenge, even if it means their own deaths. Odysseus readies himself to fight, and it seems as though a civil war is about to erupt when Athena intervenes and insists on peace.