The question is simple: will the cynical world change him (the way Batman was changed by it), or will he change the cynical world?
Clark leaves, to think and explore his own heart and worldview. A Superman forced to confront his idealism amid a cynical world is not an abandonment of the traditional characterization, it is a reinforcement of it. It shows that yes, Superman can have his beliefs and idealism challenged, and in the end even in the face of a world that doesnt want to change Superman will refuse to give up on us. In Batman v Superman, he wonders about the consequences of his actions and whether it is possible to stand for absolute good when the outcomes can often inevitably created complicated side effects.
When Clark sees his human father, Jonathan Kent, we get a story about how faced with a rising flood threatening to wipe out the family, Jonathan helped dig a trench and block the floodwaters path. He was a hero for those actions, he saved the family farm, but the digging redirected the floodwater to another farm and destroyed it. Remember that this is in Clarks mind and memory, so when he asks his father if he ever got over the bad dreams about the unintended consequences, Clark already knows the answer, because this conversation is all about Clark talking to himself. His father says yes, he was able to live with the consequences of his actions because he found faith again when he met Martha.
What is this about? Its pretty straightforward, really Jonathan couldnt refuse to act, to save his family, and he did so without any expectation that saving his family would create a flood of action elsewhere that harmed other people. The flood did that damage, not Jonathan, and all he could do all any of us can do is act to do good and save people when we see it. If we know possible consequences, then we must think through our actions and make sure to consider those consequences and how to either divert them or live with them and continue having faith. Love, and having a life to live that shows us why we must act to do good, helps us have faith in ourselves and in the world. Because however dark the world becomes, however hard it can be to accept consequences of our actions when we know were doing the right thing but the world will blame us for it, we can have someone who makes it all worthwhile, someone who represents the good we know exists in this world. And that good is always, always worth fighting for.
Superman knows he cannot give up, knows he must always act and use his powers for good, and knows that Lois is the love of his life and represents all of the people who do look to him as a symbol of hope and goodness in the world. It is a simple message, but it resonates as clearly to me as anything in the film. So he comes back, and his return coincides with Lex putting his final evil scheme into motion. Lois is thrown off the building, but Superman is already back in town and saves her. He has come back, and immediately his choice to return presents him with a final challenge to his idealism his mother will die unless he kills Batman.
It seems an impossible choice, and he remarks that no one stays good in this world, but this is clearly not literal since we see his true intention is to convince Batman to help him. He never tries to kill Batman, making it clear by literally saying it out-loud. In the end, he will die trying to convince Batman to help save Martha, rather than do Lex Luthors bidding and murder a hero he (Superman) has finally come to understand as a good man being corrupted by a cynical world (something Superman has been struggling with himself, which is why he now understands Batman).