Well the dream sequence itself was more to link the foreshadowing for the Justice League, but it served as a concrete motivator to get Superman whereas before there wasn't any mention by Bruce of getting at him. It was the final straw to a number of things from the Metropolis incident, the returned checks orchestrated by Lex while seeing the Senate building explode, and the vision/warning by Flash giving him the confirmation that he was right all along. Lex even admitted to Superman that he planted seeded at Bruce into having an obsession to get Superman. So it's everything connected leading to that. Which makes sense in real life. Not just ONE thing going to flip someone off all the time, it got to be numerous of things that you soon realize how far of a danger someone can be.
As for Superman, he is just as much in the wrong, and he knows this after the Senate explosion which he took blame for and rightfully so. As he told Lois, he wasn't looking. Dude was self-righteous and judgmental like how God (if you believe in God) would act in cherry picking who's lives to save. That was the whole issue over the African massacre. He only went there to save Lois and this was AFTER all of those people got slaughtered knowing he could of gotten there sooner. But when Lois 1st brought it up, he was defensive saying he didn't kill those people. This was why Lois initially questioned if she was a hindrance to their relationship (which, in foreshadow... she is). The problem with Superman initially, and while half the planet have a love/hate relationship is because he picks and chooses his heroism. He can save people from a burning building, or save a ship from being stuck on a sea full of ice, or save a group of people from flooding... but would ignore people massacred from terrorism or have any conviction either way in regards of criminal behavior. This is why he looks at Batman sideways because he sees him and his ethnics no better than the common criminal not even understanding what true crime and terror is like. Aside from Zod... who else have he went up against? It was messed up for him to show up all late and only showing up to save Lois in that African slaughter. This was why they held a Senate hearing to debate as to how to reign-in Superman, because he's doing whatever he wants to do without answering for his own actions or lack thereof.