The disagreement between Telemachus and Penelope arises from differing opinions on the entertainment of Phemius. Phemius is singing the tale of the Greek warriors of Troy and their homecomings when Penelope descends from her chambers to protest this choice of music. She scolds him, and orders him to stop because he has reminded her of Odysseus, whos long lost at sea. Telemachus rebukes his mother by protesting that the bard has the right to sing anything he wishes. He then sends his mother off to her chambers, declaring that he is the master of the house.
This clash between Penelope and Telemachus was caused by both. Penelopes fault was that she did not stop to consider Telemachus feelings on the subject. She is so engrossed in her own pain for her lost love that she is blind to the problems of her son. She does not see his insecurities on his past and especially his future, or his lack of confidence in himself. Most of all, she is ignorant to his inner struggle between love and hate for Odysseus. She does not realize his need to learn of his legacy, she only sees her grief and her pain.
She is very detached from the world, and focuses on her grief and pain. Because she is so preoccupied with her own problems, she has neglected her duties as a mother. She, in her distress, has pushed her son away from her. This disagreement over Phemius only shows the deep chasm that has come between them. As for Telemachus, he makes the same mistakes as his mother in that he refuses to see her side of the issue. He, too, is deeply engrossed in his problems that he does not see the deep extent of his mothers pain.
Him ordering her to leave is a sign that he believes her feelings to be almost inconsequential compared to his. His eagerness to learn of Odysseus great deeds seems to overshadow the sadness his mother feels. The tales of the Trojan War are the only way in which he can come to know his father, who he does not remember, since Penelope obviously avoids the topic entirely. He needs to know his legacy. Most importantly, he is searching for a way to justify his fathers absence, and to justify why he has left Ithaca in such a state of disorder.
However, his quest for his legacy was not the only reason he had for defending Phemius. It was also caused by his resentment towards his mother for having known his father and not telling him about him. He feels that his mother has prevented him from gaining an understanding of his heritage. This disagreement over Phemius was a window to the anger that Telemachus had towards his mother for not familiarizing him with the legacy of his father. Another reason Telemachus was so quick to rebuke Penelope was his deep desire to exert his power and his dominance, his rightful dominance over the household.
By ordering his mother to leave the hall, he is showing to the suitors that it is he, not his mother, who has more power. When he declares that he is master of the house, partially caused by the newfound courage distilled in him by Athena, he is introducing a new him. This was his opportunity to establish his position above the suitors and prepare for his announcement that he will go search for his father. This disagreement allowed Telemachus to step into the limelight, and express himself as a force to be reckoned with.
