Maybe Superman sees Robin as an innocent in need of protection. He doesn't want Batman's darker methods to harm Robin.
Superman might believe that Batman has gone too far in his pursuit of justice and that Robin is caught in the crossfire. He wants to safeguard Robin from Batman's potentially overzealous actions. Also, Superman could have a personal respect for Robin's youth and potential, so he steps in to protect him from what he perceives as Batman's more extreme tendencies.
In this fanfiction, Superman might use his super strength to physically stop Batman from harming Robin. He could also use his heat vision to create barriers or distractions.
One possible plot could be that Superman and Robin team up to stop a powerful villain who is causing chaos in Gotham City. Maybe the villain has some kryptonite - based weaponry which makes it tough for Superman, and Robin uses his detective skills to figure out how to disable it. Then they combine their powers, Superman's super strength and flight with Robin's martial arts and acrobatics, to defeat the bad guy.
One possibility is that the Justice League would be divided. Some members might side with Superman, believing he had a good reason, while others would stand by Batman. This would create a power struggle within the league.
Perhaps it's a case of a misunderstanding. Superman might think Batman has done something that endangers Metropolis, like developing a weapon that could potentially harm Kryptonians. He kidnaps Batman to find out the truth and keep the city safe. This could lead to a tense stand - off where Batman has to prove his innocence.
The fanfiction could involve Superman taking care of Batman in a more psychological way. Maybe Batman is going through a tough time, doubting his methods or his role as a hero. Superman, with his positive and hopeful outlook, tries to cheer him up. He could share stories of his own struggles with being an alien and how he found his place on Earth, inspiring Batman to reevaluate his own path.
One possible plot could be that Batman and Robin are investigating a new villain who is using chemical weapons in Gotham. They have to use their knowledge of chemistry to analyze the substances left at the crime scenes and develop countermeasures. For example, Robin uses his school chemistry knowledge to identify a rare chemical compound in the weapon, and Batman uses his resources to find an antidote.
Well, in this fanfiction, it might focus on the emotional aspect of their talk about protection. Robin could be worried about Batman taking too many risks, and they talk it out. It could also involve Robin learning new ways of protection from Batman. For example, Batman might be teaching Robin how to better protect himself during combat situations.
Well, Batman might become super protective. He could lock down the Batcave to keep Robin safe while he's sick.
One possible reason could be mind control. Maybe some villain has taken over Superman's mind and made him do it. Another reason might be a fundamental difference in their ideologies that has escalated to the point of no return.
Well, they might play on the League's weaknesses. If the League has a fear of the unknown, Batman and Robin could create situations that are full of mystery. They could leave cryptic messages or symbols around the League's headquarters that seem to imply a greater threat. Just like how Batman uses his bat - symbols to strike fear into the hearts of criminals in Gotham.