Naruto might initially be very disappointed. He has always been eager to train and become stronger. So being denied by Kakashi could make him feel a bit down. But he could also be defiant. He might start training on his own, determined to show Kakashi that he doesn't need his approval to get stronger.
He could also be confused. Naruto might not understand why Kakashi is denying him the training. He may try to talk to Kakashi to find out the reason. And if Kakashi doesn't give a clear answer, Naruto could become frustrated. He might seek advice from other people like Iruka - sensei or his friends to figure out what to do next.
One possible reason could be that Kakashi might think Naruto is not ready yet. Maybe Naruto hasn't mastered some basic skills that are prerequisites for the more advanced training Kakashi has in mind. Another reason could be that Kakashi is worried about Naruto's recklessness. Naruto has a tendency to rush into things without thinking, and Kakashi might fear that this could lead to Naruto getting seriously injured during the training.
Naruto could be confused. He may not understand why he was denied when he has accomplished so much. He might start to question the system and those in power. This could lead him to have some internal conflict as he tries to figure out whether he should continue to strive for the promotion within the existing framework or find his own path.
Eventually, Naruto could grow resentful. If the ignoring persists for a long time, he might start to think that Kakashi doesn't care about him at all. This could change Naruto's attitude towards Kakashi and might even make him more rebellious in his training or actions. However, deep down, he still probably hopes for Kakashi's recognition and approval.
Naruto would be devastated. He sees Kakashi as a mentor and father figure. He might initially go into denial, not believing that Kakashi would actually abandon him.
Naruto might also try to find alternative ways to gain strength. He could explore the forest around the village to find new training areas or discover new chakra - related phenomena. He has a curious nature, and this could lead him to stumble upon something that gives him an edge in his training, like a hidden hot spring that has special chakra - enhancing properties.
In this fanfiction, Kakashi could help Naruto in his training through mental conditioning as well. Naruto is often impulsive, so Kakashi may work on his patience and decision - making skills. He could use his Sharingan (if applicable in the fanfiction) to analyze Naruto's movements during training and give him detailed feedback. Moreover, Kakashi could introduce Naruto to different types of enemies and battle scenarios in a controlled training environment, which would broaden Naruto's understanding of combat and make him a more versatile ninja.
It could be due to the current situation in the village. There might be threats that required Naruto to stay. Tsunade, as the Hokage, had to consider the overall safety and stability of the village. So, she denied Naruto's request for the training trip to ensure he was available in case of any emergency.
At first, Naruto would probably be extremely shocked and in denial. He has always looked up to Kakashi as a mentor and friend, so the idea of being betrayed by him would be hard to accept immediately.
Naruto might be initially very disappointed. He has always looked up to Kakashi as a strong and cool ninja, and being refused by him would be a big blow. He could become a bit sulky and withdrawn, feeling like he's not good enough.
Kakashi's reaction would be complex. He is a man who has lost many people in his life. But Naruto was special. He would hold Naruto tightly, his hands trembling slightly. He might try to use some of his own chakra to keep Naruto alive a little longer, but deep down he knows it's futile. His face would show a mixture of pain, regret, and love. He would remember all the times he trained Naruto, all the lessons he taught him, and how Naruto had surpassed all expectations.