Why is Batman's name placed before Superman's in Batman v Superman: Dawn of Justice?

The film summary for Batman v Superman: Dawn of Justice from the sidebar of Googling "Batman v Superman" makes it clear that the plot is Batman/Bruce deciding that Superman is "a bad guy", a criminal.

It's been nearly two years since Superman's (Henry Cavill) colossal battle with Zod (Michael Shannon) devastated the city of Metropolis. The loss of life and collateral damage left many feeling angry and helpless, including crime-fighting billionaire Bruce Wayne (Ben Affleck). Convinced that Superman is now a threat to humanity, Batman embarks on a personal vendetta to end his reign on Earth, while the conniving Lex Luthor (Jesse Eisenberg) launches his own crusade against the Man of Steel.

The film title appears to be following the precedent of legal cases, which are always listed as "Plaintiff v Defendant". The entity filing charges is first, the entity being charged with the offense is listed second.

Possible Explanation

Batman has generated a strong interest post Nolan's trilogy that grossed a staggering total of $2.460 b in its Box Office run which means an average of $820 m. While Man of Steel even with one of the strongest buzz of the year it released, it made $668 m which is relatively less in terms of what DC characters are used to. The film barely made more than Thor: The Dark World, which was considered a glorified “time out” entry in the Marvel Phase 2 narrative. A lot of that could be attributed to the disappointing story structure and under developed characters.

Now if this is to be carried ahead in a sequel, marketing with the same name adding just the suffix of "part whatever", would mean carrying the ill-will forward to which audience wouldn't be so excited. So a smart marketing move would be to use the already popular Batman tag to it, and capitalize on the interests of the public to draw more eye balls. Now if the Batman tag is added after Superman, it would clearly mean its a Man of Steel sequel considering it happens after the events of Man of Steel, but having it in the front would mean a whole new different stand alone film serving up as an introduction for a number of characters for the long line-up of films that awaits, especially, The Justice League. In fact they have even used the "Dawn of Justice" subtitle to make it crystal clear about the leading up to Justice League thing, instead of seeing it as the sequel, hence removing every bit of the disappointment formed in the previous one from Snyder.

Why is the movie 'Batman v Superman' not called 'Superman vs. Batman'?

It is because

Batman strikes first!

Yes, almost in every I noted down 54 different scenes in the movie and the whole movie can be divided into these 4 parts.

1. The buildup.

   It mainly shows Bruce when Superman was fighting with Zod. So, the movie begins with Bruce, the gunshot at his parents and his perception of Superman's uncontrolled power. At Lex Luthor's party, Bruce Wayne is also shown interacting with Diana Prince(Wonder Woman).

2. The rivalry.

   It builds up a bit slow, and is mainly a filler. Lex was shown to be behind this. He keeps sending hurting letters to Bruce Wayne. He defames Superman by ordering his men to kill people where Superman was supposed to arrive. Also he blasts up the court/senate where Superman was present, to show some kind of involvement of Superman in the crime.

3. The Demon.

   The main demon i.e. the Joker+Riddler mixed up Lex Luthor messes up with everything, he's shown to be behind everything. His main motive is to defeat Superman but Batman gets more of his attention when Batman steal Kryptonite from his lab. ( It is somewhat apparent that he knew Batman was going to steal it, and he let him do that. So, he knew about the secret identity of both of them. Mastermind!)

4. The real Batman vs Superman

   In this part, Batman wins handsomely over Superman and was about to kill him when Lois interrupted ( though Superman could have killed Batman when he had the chance. ) But it was not about their fight, rather it was figuring out the real enemy. (it was too dramatic I believe, could have done better)

5. The final fight

   The crux of the movie is that scene in which Batman spares(had to use this word) Superman when the latter one utters the word 'Martha'. When Batman fails to kill Superman, the doomsday is produced by Lex( by using some Kryptonian regeneration technology) and is beaten by the DC trinity.

6. Towards the Justice League

   Cameo/Bonus: Justice League in Making. The seed of this is planted when Batman talks with Wonder Woman after something very tragic happens. Two clips of other meta-humans( The Flash and the Aquaman) were also shown.

Thus, the main plot revolves around Batman affecting the life of Superman and thus beginning to make a superhero team with at least 7 members in it i.e. The Justice League.