Naruto had been pestering Jiraiya nonstop, but the moment he heard that the Pervy Sage had arranged for Yoru Machi to serve as his temporary teacher and take him out on a mission, he immediately stopped making a fuss. He even bragged about it to Sasuke and Sakura.
Sasuke had not yet defected from the village, so Sakura herself did not feel much urgency about becoming stronger.
But Sasuke was different. When he heard that Naruto would be going out with Yoru Machi for special training, he was immediately tempted. He sought out Kakashi and asked to join the mission as well.
Sasuke's thoughts were simple. He wanted to use this mission as an opportunity to ask Yoru Machi for guidance.
When Orochimaru and the Sand Village had invaded Konoha, Yoru Machi's strength had been witnessed by the entire Konoha Village.
He did not need to learn all of Yoru Machi's abilities. Even possessing one-tenth of Yoru Machi's strength would be enough for Sasuke to believe he could successfully avenge himself.
Kakashi was quite helpless in the face of Sasuke's request. He knew his own influence might not work with Yoru Machi, so he went to Rin instead.
Both Kakashi and Rin understood that compared to Obito, Sasuke's obsession with avenging the Uchiha Clan was much stronger.
After all, the one who had slaughtered the Uchiha Clan was Sasuke's own older brother, Uchiha Itachi. Obito had some sense of belonging to the Uchiha Clan as well, but after his grandmother passed away, he had practically become an outsider on the fringes of the clan.
For Obito's only remaining clansman, Rin also deeply sympathized with Sasuke's circumstances, so she went to plead with Yoru Machi.
As for Yoru Machi, he had not wanted to bring anyone along in the first place.