Maybe he wants to surprise his opponents in battles. He could be waiting for the perfect moment to reveal his full power and turn the tables on his enemies.
Maybe he wants to protect his loved ones. If his enemies know his true strength, they might target his friends and family to get to him. So, by hiding his skills, he can keep them out of harm's way while still being able to fight when necessary.
Perhaps he has hidden the full extent of his Sage Mode abilities. He might be able to stay in Sage Mode for a much longer time than he has shown so far, or have some other undisclosed powers within that mode, like the ability to sense enemies from much greater distances.
Another possibility is that Naruto has a plan that requires him to keep his skills hidden from everyone, including Hinata, for a while. He could be waiting for the right moment to reveal them and use them to surprise and save the day, especially when it comes to protecting Hinata from a big threat that he anticipates.
Well, he might use simple distractions. For example, he could create a minor commotion to draw attention away when he's about to use a particular skill subtly. Maybe he pretends to be clumsy or make a small mistake on purpose so that others don't suspect he has advanced skills.
Perhaps Naruto is waiting for the right moment to reveal his skills for maximum impact. He could be planning a big surprise for his enemies or wants to make a grand entrance at a crucial time. For example, in a major battle against a powerful foe, he could suddenly unleash all his hidden skills and turn the tide of the battle, which would be more effective than showing them off gradually.
One possible reason could be that his eyes hold a special power that he doesn't want others to discover easily. For example, it might be a new type of Sharingan or a unique ability related to his Uzumaki heritage that he needs to keep secret to protect himself or those around him.
One possible reason could be that he doesn't want others to pity him. Naruto has always been a proud and strong - willed character. His scars might be a reminder of painful past experiences, and he prefers to deal with them privately rather than showing vulnerability to others.
Maybe he wants to blend in better. If he's in a situation where he needs to gather information undercover, showing off his skills would blow his cover. So he hides them to seem like an ordinary person until the right moment to strike.
Another reason could be related to his personal growth. He might be trying to master the power of the eye in private. Naruto has always been one to face challenges alone at first. By hiding his eye, he can focus on understanding and using its power without distractions or the pressure of others' expectations.
Well, in fanfictions, often the plot takes a different turn. Naruto might hide from his family because there could be some sort of misunderstanding. For example, there could be false rumors about him being involved in something bad. And he might think that his family would believe those rumors without giving him a chance to explain. So, to avoid the immediate confrontation and judgment, he chooses to hide.