One of the Dark Knight's key character traits in Batman V Superman was his fear and hatred of the Man of Steel. By the time the film had started, Bruce had been retired for some time, but decided he needed to don the cape and cowl once more when what he sees as an alien threat comes to earth.
This angrier, more brutal Batman only has the destruction of Superman in mind and, in typical Batman fashion, lets little stand in his way. As time goes on, however, Bruce comes to realize that this visitor from far away has only Earth's best intentions in mind, and he was wrong to doubt him. Still, many of his initial worries are completely reasonable, and he shouldn't forget them entirely.
Right: The Opening Scene
The first present-day scene in the movie shows Bruce Wayne rushing through Metropolis, as Superman and Zod have their vicious battle from the climax of Man Of Steel. From Bruce's perspective, he sees two powerful beings leveling a city full of innocent people. Bruce's own tower comes crashing down with his employees still inside, and he soon finds a young girl alone in the street who lost her parents.
Bruce looks to the skies and sees the man he feels is responsible, and it is here that he decides it is time to suit up once more. From Bruce's point of view, it is completely understandable the anger and fear he feels in this moment, and it is completely warranted.
Wrong: Superman's Sacrifice
The moment Bruce realizes how good of a person Clark was and regains his lost hope in humanity is when Superman gives his life to stop Doomsday. This sacrifice is what the following DCEU films were built upon, and what makes Bruce realize how wrong he was. Essentially being a mutated clone of Zod, the trinity realizes the only way to stop the creature is with a Kryptonite spear Bruce intended to use on Clark.
The only one who stood a chance to get the spear close enough to Doomsday, is Kal-El, which he does without hesitation, at the cost of his life. Bruce decides to track down other metahumans to start a team to defend Earth from threats he alone can't handle, all in the name of Superman.
Right: Superman Returns
When the heroes decided to resurrect Superman in Justice League, it looks to be a big mistake. The Superman that first awakes is not the man that died fighting Doomsday, but instead a confused and angry Kryptonian with a grudge. He holds off most of the League without breaking a sweat and targets Batman directly.
He doesn't remember who Batman is, he just knows they were fighting, and he intends to finish it. If not for Lois returning to remind him who he really is, Superman could have easily disposed of the Justice League and would have been let loose on the Earth. This confirms Bruce's fear that Superman is more than capable of destruction if he so desires.
Wrong: Zod Was Responsible For Metropolis
When Bruce looks to the sky and sees Superman, he blames him directly for the carnage and destruction of Metropolis. What Bruce failed to see at the time, was General Zod was the culprit and Superman only wanted to save the city. From an outsider's perspective, it just looks like two God-like beings fighting with little regard to human life, which is not the case.
Superman feels immense guilt for what happened to his city and even has to force himself to kill his foe to save a family, which he feels equally guilty for. If given the chance, Superman would have taken the battle far from the city, but Zod gave him little choice.
Right: Superman Can Bring Earth To Its Knees
While he has a good heart and is Earth's defender, Superman would have no issues ruling the planet if he so desired. When Bruce first learns of Superman, he believes anyone with this level of power can be corrupted and will eventually wipe out the planet. Bruce is right in that with his powers, Superman could easily level the planet with little opposition.
Even the mighty Justice League would have a difficult time stopping a murderous Superman at full power. Bruce may have been wrong about the man, but he is right to fear the power that Kryptonians hold in the presence of Earth's yellow sun.
Wrong: Superman Does Not Wish To Be Worshipped
The phrase "God" or "God-like" is often used to describe Superman, but this is the farthest thing from what he wants. Superman is humble and sees himself as a protector of Earth, not a ruler. While his powers are certainly God-like, Superman puts a block on them, meaning he is rarely at full power.
This ensures the safety of the planet and makes sure he never crosses the line of hero and villain. Superman is fully aware of his powers, but what Bruce may not know, is that Clark is just as afraid of them, if not more. He knows that one wrong move could mean life or death, and is constantly terrified of making it. Clark was raised by humans, and in his eyes, that's what he is.
Right: He Brings Threats To Earth
While Superman himself does not pose a threat, his existence does. Bruce fears Superman because he feels he will bring danger to the planet, which he does albeit indirectly. Zod is responsible for the destruction of Metropolis, but he never would have thought to come to Earth if not for Kal-El.
Superman will give his life for Earth, but so many lives would have been saved if he never came to begin with. In the long run, Earth is better off for his presence, but one could also argue they would be safer without him. To many, he serves as a target on the planet to threats that want a piece of the last Kryptonian.
Wrong: He Lost His Home Once
Bruce is afraid Superman will see Earth destroyed, but what he doesn't realize is Superman views Earth as his home, and he has already lost one before. Kal-El may not remember his homeworld of Krypton, but he still feels remorse for not being able to save it. As an adult, he realizes that Krypton was always doomed and he couldn't have saved it even if he was there, but he is on Earth.
Superman understands that while born on Krypton, Earth is his home, and he isn't about to let it go without a fight. Bruce at first only sees a menace, but Clark sees an opportunity to save his home.
Right: The Future Shown In Justice League
In the final scene of Zach Snyder's Justice League, audiences are shown what could eventually come to pass. Darkseid arrives on Earth like he promised, and enlists Superman to help. Superman takes over the Earth with ease and leaves the Justice League to travel the wasteland in hiding.
This future is exactly what Bruce feared, and his fears are more than warranted. The once symbol of hope is a feared ruler who will waste no time in destroying anything or anyone to get what he wants. While seen as an alternate reality, it is a reality where Bruce was right about Superman from the very beginning.
Wrong: His Existence Protected Earth
While he unwillingly brings threats to Earth, Superman's existence also protects Earth from more sinister beings. It is known across the universe how powerful Superman is, and what he will do to protect Earth.
The thing that kept Darkseid from returning to Earth, was Superman. His death echoed far wide, alerting outside threats that Earth was up for grabs. While Bruce originally believed Superman would bring the planet's downfall, he failed to understand that he was the only thing protecting it from the greatest threat of all.