Reviews and breakdowns of the recent Batman vs. Superman: Dawn of Justice trailer have unraveled interesting fan theories, plot devices, comic book references, and philosophical ideologies. But one aspect I have personally questioned at times is this so called "enemy" Alfred Pennyworth (played by Jeremy Ions) talks about. Many say that it is Superman, of course... but there's another option.
During the trailer - roughly around the 2 minutes and 42 seconds mark - Alfred is speaking to Bruce; persuading him that someone is not their "enemy." There's a possibility that he is talking about Lex Luthor, the owner and reigning president of LexCorp.
The interesting thing to address is: In most trailers put out these days, if there is a character talking about an enemy or villain in one scene, the next would immediately lead to another showing the nemesis. In this trailer, however, the scene is not followed by the Man of Steel, instead, we are shown a glimpse of LexCorp.
What does this mean? Well, for one, Lex Luthor has huge significance in the plot of Batman vs. Superman. He is essentially the one who causes the pivotal clash between the two characters, all for his own personal gain - which is a nice reference to many incarnations of Lex, where his business egocentricity forces him to put himself before any other.
Another implication comes in the next shot: We are shown Lex walking over scattered bullets, later gazing his eyes on Kryptonite. If you know from comic book history, Superman's weakness is Kryptonite, and Lex is notorious for treasuring the element as a method of overpowering him. Just remember, we are still unaware how Batman obtains it as a method for destroying Superman. Does he, somehow, negotiate with Lex to use the Kryptonite? Does he steal it himself?
Either way, it's debatable as to who Batman's real enemy is. Lex uses devious methods to prove his points, and maybe lending Batman some Kryptonite is his way of showing Superman his supremacy and that he is truly against him.