In The Odyssey, why does Telemachus return home in secret and why does Odysseus hide his identity from everyone but him?
While Odysseus (Ulysses) does only reveal his identity to Telemachus at first, it is not Telemachus who returns home in secret. Instead, it is Odysseus. Telemachus has been traveling to try and find his father, to stop the many suitors from wooing Penelope; Telemachus considers them to be "parasites" and holds out hope that Odysseus is still alive. Odysseus is disguised by Minerva (Athena) and so is revealed to Telemachus at the house of a swineherd, after which they hatch a plan to infiltrate and destroy the suitors before there is any suspicion.
"Now, therefore, return home early to-morrow morning, and go about among the suitors as before. Later on the swineherd will bring me to the city disguised as a miserable old beggar. If you see them ill treating me, steel your heart against my sufferings; even though they drag me feet foremost out of the house, or throw things at me, look on and do nothing beyond gently trying to make them behave more reasonably; but they will not listen to you, for the day of their reckoning is at hand."
(Homer & Butler, The Odyssey, gutenberg.org)
While Odysseus has extraordinary skills and strength, and while he is backed by certain of the Gods, he is also only one man. Odysseus has not survived this long by being foolhardy, and so he plans to attack the suitors without their prior knowledge or preparation. Also, at this point, Odysseus cannot be sure who to trust; he knows that Telemachus, his son, is trustworthy, but others may be allying themselves with the suitors with the assumption that Odysseus is dead. By enlisting Telemachus's help, Odysseus is able to get closer to the suitors -- and Penelope -- than before; he is thereby able to get his hands on his mighty bow and fight alongside Telemachus to rout the suitors and regain his throne and wife.
Telemachus goes out to find out the trith about Odysseus' birth...and that he had been sent out to be abandoned to die on a mountainside because his father feared the oracle telling him his own son would kill him. Telemachus discovers the truth,,,Odysseus has sworn to kill whoever is responsible for the curse upon his people...the person who killed the king. He discovers it is himself...But does not want to hear it!