Why do Telemachus and his mother need Odysseus?
Penelope has little status and no power as a woman, though she does have great wealth. Telemachus, though he is now over 20, has never proven his manhood. In one respect, neither "needs" Odysseus. Penelope could agree to marry the least offensive of the suitors, and would thus provide Telemachus with a step-father. But that is not Odysseus' fate, and such a conclusion would have been repugnant to the Greeks.
Telemachus and his mother need Odysseus so that they can rid their house of the suitors that eat their food and drink their wine and waste their goods. Without Odysseus Telemachus' mother Penelope cannot get rid of them without choosing a suitor. Although she did not want to remarry any of them, with her husband gone for ten years, she has no choice but to consider them, and no way to get them out of her home.