One possible reason could be that his sister has some special or unknown powers that Naruto doesn't understand. For example, if she has a very unpredictable and potentially dangerous kekkei genkai. Another reason might be that she has a very strong and intimidating personality, which makes Naruto feel small and scared in her presence.
Maybe it's the high expectations that Naruto has for Boruto. Naruto is a hero, and he might unknowingly put a lot of pressure on Boruto to follow in his footsteps. Boruto could be scared of not being able to meet those expectations.
One possible reason could be that Kushina has a very strong and intimidating personality. In the Naruto universe, she was known to be a tough kunoichi. Naruto, who might be used to more gentle or reserved people around him, could be scared of her boldness.
One possible reason could be some past trauma. Maybe he had a bad experience during a battle or an encounter that made him associate touch with danger. For example, if he was once grabbed forcefully by an enemy during a fight and it led to a near - death experience, that could make him scared of touch.
One possible reason could be that Naruto has heard some spooky stories about Kushina from the past. Maybe there are tales in the village that at night, Kushina had a more intimidating presence due to her strong personality and powerful chakra. Another reason might be that Naruto has some sort of premonition or nightmare related to Kushina at night, perhaps linked to some hidden family secrets or events that he is unconsciously aware of.
It could be due to a misunderstanding. Perhaps there was an incident where his sister was involved, but Naruto misinterpreted her actions as something malicious against him. Like she might have accidentally broken something precious of his and he thought it was on purpose.
One possible reason could be Kakashi's reputation as a strict and powerful teacher. Naruto might be in awe of his skills and fear making mistakes in front of him.
It might show Naruto's vulnerability. Usually, Naruto is seen as a brave and determined character. But being scared of his sister reveals that he has his own insecurities. This can add depth to his character as it shows he's not just a fearless hero all the time.
One reason could be a past bad experience. Maybe he had a really painful treatment as a kid that left a deep mark. For example, if he had a serious injury once and the doctor was rough while treating him, it would make him fear doctors.
One possible reason could be to protect her. Naruto might believe that by leaving, he can draw danger away from his sister. For example, if there are powerful enemies targeting him, he doesn't want his sister to get caught in the crossfire.
One reason could be Kakashi's Sharingan. It's a very powerful and somewhat spooky ability. Naruto might see it in action in a way that scares him. Maybe Kakashi uses it to subdue an enemy in a really intense way that makes Naruto realize how dangerous Kakashi can be.