Well, Naruto is a passionate character. If he gets pissed on fanfiction, he could confront the writer of the fanfiction in some really creative ways. He might use his shadow clones to surround the writer's fictional self and demand an explanation for whatever has made him angry. He could also try to rewrite the fanfiction himself if he has the power to do so in that fictional universe, to make it more to his liking.
In fanfiction, when Naruto gets pissed, he might decide to leave the village that he's in within the fictional story. He'd feel betrayed or frustrated, and think that leaving is the best option. This could lead to all sorts of new adventures and storylines as other characters try to find him or he tries to find a new place to belong.
Maybe he'll go on a rampage in the fanfiction world. He could start using his powerful jutsu to show his anger, like unleashing a Rasengan on the source of his annoyance.
Sasuke could be the cause. If Sasuke were to betray Naruto again in the fanfiction, it would surely make Naruto pissed off. Their relationship is complex and Sasuke's actions have a big impact on Naruto.
He could use his ninja skills to fight back. Naruto has a wide range of jutsu at his disposal, like the Rasengan. So, he might quickly launch a counter - attack to protect himself.
Sasuke could be a possible cause. If Sasuke were to go back on his word about protecting the village or if he were to harm their friends again, Naruto would be pissed. Their relationship is complex, and Sasuke's actions often have a strong impact on Naruto.
A new, powerful and arrogant villain introduced in the fanfic could be the cause. This villain could constantly mock Naruto and his ideals, and try to undermine his efforts to protect the village. Such blatant disrespect would make Naruto really pissed off as he is very protective of his home and the values he stands for.
One scenario could be when Naruto finds out that someone has been spreading false rumors about his friends. This would surely make him pissed as he values his friends deeply.
In fanfiction, when Naruto gets called by the council, he might be faced with various challenges. Maybe they will question his loyalty to the village again, despite all he has done. It could also be that they want to assign him a difficult mission that only he can do because of his unique abilities.
Naruto might get hurt during a mission with Kaka - naru. Kaka - naru could then carry Naruto back to safety and tend to his wounds. This simple act of care can strengthen their bond.
In some fanfictions, when Kakashi finds Naruto, it could be a situation where Naruto is in danger. Kakashi would then rescue him and from that moment on, their bond becomes even stronger. Kakashi might then focus on helping Naruto control the Nine - Tails' chakra more effectively, which would change the course of Naruto's development in the story.
One reason could be betrayal. If someone he trusted, like a fellow ninja or an old acquaintance, turned out to be working for his enemies, that would surely make him pissed. It's a huge blow to his trust, which is a big part of his character.
Well, in a 'naruto gets pissed fanfic', Naruto might get angry over various things. It could be because of an enemy taunting him about his past, like how he was an outcast in the village as a child. He could also get pissed if his friends were in danger and he felt powerless to help them right away.