Actually you raise an issue that was to me once something that I
took issue with same as you have. Superman has literally
saved the entire world. And Batman is truly a genius detective on the order of a Sherlock Holmes. How would he come to the conclusion that Superman poses such a grave threat? Conceptually that did not square for me. So I came up with my own theory:
1) Batman by now has become as cynical as can be about the military industrial complex and the evil things that are done in the name of "defense"; and he sees Superman's possible alliance with the military as a threat (an uneasy and loose working relationship, but still agreeing to work with them for some things for which he is truly needed),
2) Superman's apparent decision to leave the scout ship in the military's hands (which was just monumentally bad judgment--as we see with what Lex does with it), and
3) the conflict between the two being cued by Amanda Waller directing Swanwick to ask Superman to set limits in Batman (because Batman risks mucking up her A.R.G.U.S. plans); i.e., she knows Batman is likely to go on a suicide mission against Supes if that were to happen.
But in some conversations with other about this in the above linked thread, I realized that while the above theory would be more satisfying to me intellectually, it would probably be too cerebral for the GA.
I had also observed in earlier formulations about Bruce's reaction that there are some really major psychological issues that Bruce has that are tweaked by all this. Helplessly watching 5000 people die during the Black Zero event as two god-like aliens duke it out taps the helplessness that he felt as a child. What Batman ultimately struggles with the most is how to control the rage that stems from his experience of helplessness as a child at his parents' having been murdered before his eyes. In Batman: Earth One (from which it seems BvS's Alfred is drawn) you see also that Bruce's childish impulsivity and self-centereness directly leads to his parents' death, even though by chance. So I think it's reasonable to infer that as a child he felt not just helpless to prevent, but also directly responsible for, his parents' murders as well. Batman, both as as an identity and a life-style, is a way of controlling and directing his rage at that helplessness. His darkest fear is to lose control that rage (which gets translated adaptively for a crime-fighter into his hyper-vigilance/paranoia, thinking five steps ahead of opponents, always developing contingencies, etc.). The nightmare dream that Batman has includes a scene of him snapping a neck (breaking his no-kill rule) which I feel is an unconscious association with Superman having snapped Zod's neck (i.e., Supes also traditionally has a no-kill rule). The neck-snap merges the two of them symbolically. The evil tyrant Superman that appears in Batman's dream is a projection of what Batman fears most about himself: that he has, sadly, indeed become a "one-man reign of terror." The crisis that he's going through is that all that he has worked for as a crime-fighter over the course of his life is 1) now rendered obsolete and irrelevant by god-like beings and an extinction level event, and 2) ultimately a sham in that he has become not so different after all than the thugs that he hunts down.
Anyway, even if I don't have every detail right there, the accumulated force of something along those lines has precipitated a kind of a breakdown for Bruce. I'm pretty sure I recall reading that Ben Affleck has alluded to this in more than one interview. (See
this for one salient Affleck quote.)
Anyway, it's looking more to me now that Snyder probably went the more psychological and emotional route to explain why Batman essentially goes on a suicide mission to take out Superman. I still hope the story will also include something along the lines of my conjecture about why Batman would fear Superman's potential for evil from a more rational perspective. But it's okay with me now that Batman is being portrayed as more human and vulnerable to his own demons. It's actually better drama, imho. It will connect better with viewers in the theater (the vast majority of whom are not CBM or comic book nerds like us).
)--so he continues to express reservations about how well Gal will do, but he also grudgingly admits that she seems to be looking pretty convincing in the role from the glimpses we have seen, and 
