From the book of Odysseus why does Telemachus and his mother need Odysseus?
They need his strategic planning, his thirst for revenge, his patience, his ability to string his bow, and help from the god Athena to defeat the suitors.
Penelope has tried to trick the suitors with her cunning. She has kept them at bay by weaving the shroud. Her cunning is impressive, but the suitors are wise to it. She has bought time, but her plan cannot make them go away.
Telemachus is too impetuous and brash to defeat the suitors alone. They will kill him easily. He cannot string his father's bow. He does not possess the magic of Odysseus' cunning yet.
Only with Odysseus, can Telemachus defeat the suitors. Penelope doesn't even know Odysseus is on the island. She is not part of his plan. Revenge is not woman's work.
Remember, Odysseus is not coming to the island alone. He is bringing Athena with him. She disguises him as a beggar. If he shows his face, he will be killed instantly. So, his plan of revenge is ordained by the goddess. It can only be accomplished with help from the gods: this is the lesson that Odysseus has spent 10 years learning.
Odysseus rallies his son and his troops, the herdsmen. He exercises cunning and patience in his plan. He traps the suitors all in his hall, lures them there with a false promise: he who can string the bow will become king. His plan of revenge is as cunning as his plan to end the Trojan War with the wooden horse. After he strings the bow, his identity is finally revealed and he and Telemachus kill them in a river of blood.