Another possibility is that Naruto and Yang have a special bond. This bond could be formed through shared experiences, like they both went through a difficult training together or survived a life - threatening situation. Because of this special connection, Naruto feels indebted to Yang or simply values Yang's life more than his own arm.
One possible reason could be a sign of extreme loyalty and friendship. Naruto might see Yang in a dire situation where she needs his arm for some crucial purpose, like to complete a powerful jutsu or to defend against an overwhelming enemy. He is known for his selfless nature, so sacrificing his arm would be in line with his character.
Maybe he was protecting someone in Wave. He's always the self - sacrificing type, so he could have put himself in harm's way to save a villager or a friend.
It could add a lot of drama. The sacrifice of a limb is a huge deal, and it would change Naruto's abilities and his role in the story. It might make him more of an underdog, which could lead to new character development as he has to adapt to his new physical state.
It could be related to a mission. Suppose Naruto's arm has some special power or ability that is crucial for a mission, but Sakura disagrees with how Naruto is using or handling it, thus causing the confrontation.
She might become more cautious. Having received Naruto's arm, she realizes the great sacrifice he made. This could make her think twice before engaging in battles recklessly, as she now has a part of someone she respects and doesn't want to waste this 'gift'.
Perhaps he meets an ancient sage or a hermit who has the knowledge of regeneration. This character could guide Shino and provide him with the necessary herbs, incantations or mental exercises to regrow his arm. It could be a spiritual journey for Shino as he has to prove himself worthy to receive this knowledge.
Maybe he was in a dangerous duel with a powerful dark wizard. The dark wizard could have cast a spell that was specifically designed to maim or disarm in the most literal sense.
Another scenario might be that Naruto sacrifices his arm to save someone he cares about deeply. He might have used his arm to block a fatal attack aimed at a friend or a loved one, showing his selfless nature even in a fan - created story.
In the context of the fanfic, it could also impact his relationships. His friends might be overly protective, which Naruto may not like. Or, he could inspire others with his determination to keep going despite his injury. It might also change how he is perceived in the ninja world. Some may see him as weakened, while others could view him as even more of a hero for his ability to persevere.
Sasuke could be a candidate. Given their complex relationship, Sasuke might find a way to give Naruto a new arm as a way to atone for their past differences. He could have discovered some rare medical ninjutsu during his travels or come across a powerful artifact that he uses to create a new arm for Naruto.