The team might abandon Naruto if they are faced with a difficult choice where they think sacrificing Naruto is the only way to save the village. They might believe that Naruto has some connection to an enemy that they can't overlook. Or it could be that jealousy plays a role. If Naruto starts to gain more power or recognition than the rest of the team, they might become envious and abandon him out of spite.
One reason could be that his team discovers some kind of hidden power in Naruto that they fear. Maybe they think he's too dangerous to be around, so they abandon him. Another possibility is that they are influenced by some outside force, like an enemy who convinces them that Naruto is a liability.
In the fanfiction, perhaps Naruto makes a big mistake during a mission that endangers the whole team. His team, being unable to forgive him for that, decides to abandon him. Or it could be that there is a prophecy related to Naruto that the team misinterprets as something bad, and they abandon him to protect themselves from the perceived threat.