Batman’s mission is avenging his parents.
That’s what writers do when they make a character, that character never starts as a blank slate. The problem is that the character Batman has precedence so contrary to what Snyder actually presents.
Certainly I would say Snyder does although shabbily justify why his Batman is so angry, he lost his kid partner to a violent criminal. Batman had lost faith in his way of justice, in letting bad guys live they just eternally do the same crimes.
The core problem of the movie is why Batman and Superman come into conflict at all, and why Batman and Superman don’t just talk it out considering one is a genius, and the other is emotionally genius and simultaneously very communicative.
An actor will always fall short if the script does.
Batman branding people can make sense, but is it really Batman at that point? The integral change to the character means on some level the writer has to justify the new canon to the hardcore Batfans.
I don’t think Batman’s behavior has anything to do with Superman. Batman wants to eliminate evil, Superman can do what Batman wants, but even better . The movie makes a false leap by having Superman try to stop Batman, and Batman preparing for a battle he could otherwise entirely bypass. Batman has a huge ego to think he can overcome Superman, and I think that in itself is typically canonical, but Batman shows a huge lack of intelligence in not trying to subvert the fight. Batman is always a genius, yet here he’s not.
Superman fights Bruce because Lex has his mother, blackmail. Bruce fights Superman because…no reason, he doesn’t have to. They are not even at irreconcilable odds yet still the fight happens: as proven by Man of Steel even Superman can understand sometimes murder is necessary for permanent, greater good.
Ultimately the movie just doesn’t make sense because it contradicts itself plot point by plot point, makes iconic characters into things they are not, and doesn’t let characters act naturally. People tend to talk first then throw fists.