What is Telemachus's problem in The Odyssey? I want to know what are the problems that Telemachus encounters while Odysseus is not around.
Telemachus is at a difficult age. He's on the cusp of manhood, but without a man about the house he feels somewhat lost. He wants to become a great warrior king just like his father, but without Odysseus's fatherly guidance he's unable to step up to the mark. What's particularly galling for Telemachus is that the honor of both his parents is being insulted every single day by the importunate suitors. He'd love nothing better than to drive them out of the palace, but he's too young and too inexperienced to do so. Telemachus sorely needs to become a man.
Telemachus is certain that Odysseus is dead, even though in reality he's still very much alive and well. But it's important that the gods don't let on to Telemachus the true fate of his father. The goddess Athena is enormously helpful to Telemachus, giving him courage and pointing him in the right direction. But she doesn't want to do everything for him; it's part of the gods' grand plan that Telemachus becomes a man on his own steam—that he proves his strength, tenacity, and courage in the same way his father did.
Telemachus's most significant problem, besides the continued absence of his father, is that the suitors who are attempting to woo his mother, Penelope, are exploiting his hospitality and eating him out of house and home. In ancient Greece, people believed that Zeus protected travelers and mandated that great hospitality be shown to anyone in need of it. The suitors are really abusing this belief, making free to drink Odysseus's wine and slaughter his livestock for daily feasts. This has gone on for years because they believe Odysseus to be dead, and they all want to marry his widow and take his great house and lands and goods. In addition to simply wanting to know what happened to his father -- even if the news is that Odysseus has died -- Telemachus needs to find a way to rid his home of these suitors. When Athena, in disguise, tells him that his father is living and sends him in search of news, the suitors actually plot to kill him upon his return.
The largest problem that Telemachus faces in Odysseus's absence is trying to be the man of the house before he is seen to be a man. The suitors are taking advantage of his mother's hospitality, the servants at the home, the food, and the land. He wants to protect what is his family's and his. He cannot, however, easily stand up to the suitors who are all seen by society as men. They have proven themselves through wealth, bravery, and other means, whereas he is still seen as a child.