How does Telemachus's hesitancy to speak to king Nestor demostrate that he is wise in his own way too?
Odysseus, according to the Odyssey, has been away for twenty years. Telemachus, now a young man, wants to learn about his father's whereabouts. So, he heads off on his own mini-odyssey. This shows that he is growing up and becoming a young man in his own right.
When he and Mentor (Athena in disguise) come to old Nestor, Telemachus is cautious. This shows that he is wise. He knows of Nestor's reputation as a wise man and a great conversationalist. Moreover, Telemachus has good self-knowledge. He knows that he is young and inexperienced. So, he rightfully considers the best way to approach Nestor. This hesitancy is rooted in wisdom. Only a fool does not consider the situation. Athena, in disguise as Mentor, encourages him, and so Telemachus goes and he is welcomed warmly.
Here are the words that Telemachus speaks:
The prince replied, wise in his own way too, “How can I greet him, Mentor, even approach the king? I’m hardly adept at subtle conversation. Someone my age might feel shy, what’s more, interrogating an older man.”