One possible reason could be to protect them. In many fanfictions, Harry might believe that by distancing himself from his friends, he can keep them out of danger. For example, if there is a new dark threat targeting him specifically, he may think that the enemy will use his friends against him.
Some of his friends could be inspired. They might see Naruto's departure as a noble act, especially if he's leaving to protect his family. Naruto has always been a source of inspiration, and this could lead them to re - evaluate their own relationships and responsibilities. For instance, Sakura might be motivated to be stronger to support Naruto's family in his absence.
Sakura would be heartbroken. She has deep feelings for Naruto, and his sudden departure would make her feel abandoned. She might initially be angry at him for leaving without saying goodbye but would soon worry about his safety.
Shikamaru and the others from the Rookie 9 would be shocked. They have always counted on Naruto to be there in Konoha. They would probably feel a sense of loss and also a bit of guilt, wondering if they could have done something to prevent Naruto from getting so tired of the village. They might try to find ways to get him back, while also respecting his decision if he is determined to leave.
Maybe his friends betrayed his secrets. In many fanfictions, a friend might accidentally or deliberately let out something Harry had confided in them, like his fears about Voldemort or his feelings for a certain girl. This could shatter his trust.
Maybe his friends in the fanfiction betrayed his trust. For example, they could have broken a promise to him, like not showing up when he really needed them. This would make Harry feel let down.
Well, perhaps one interesting moment could be when they are in a dangerous situation in the fanfiction. Harry might use telepathy to quickly communicate a plan to his friends without the enemy noticing. For example, he could send a mental image of a secret passage they can use to escape.
Telepathy likely deepens their relationships. They can understand each other on a more profound level. For instance, they can immediately know if a friend is in distress without having to say a word.
Some friends might feel betrayed. If they are very clan - oriented, they could see Naruto's leaving as a sign that he doesn't value the clan and by extension, their friendship. However, his true friends like Sasuke or Sakura might understand his reasons. Sasuke, who has his own issues with his clan, might be more empathetic. Sakura, who has seen Naruto's determination, could support his decision in the long run.
One possible scenario could be that Harry leaves his parents due to a mysterious prophecy that he needs to fulfill away from them to keep them safe. Another could be that he discovers a hidden power within himself that he can't develop while staying with his parents, so he decides to leave.