Why does Odysseus not want his presence revealed even to his family and household?
Odysseus has to plan carefully so that he will be able to exact his revenge against the suitors who outnumber him enormously. If his identity were known, they would quickly kill him so that one of them could become king. Telemachus knows who the old beggar is, and Odysseus eventually reveals himself to Eumaeus and Philoetius because he needs some assistance. Athena, however, will be his greatest source of aid when he and his team slaughters the suitors. Secrecy is essential.