If Superman kills Batman, then Batman proves his point and humanity turns on Superman. Superman has to defeat Batman by apprehending him, unmasking him and turning him over to the authorities. Superman will also have to be much more judicious with his abilities after destroying half of Metropolis in Man of Steel due to the public backlash. He can't go full on god mode unless the threat warrants.
Batman on the other hand is out to kill Superman because he perceives him to be a threat to humanity. Batman doesn't give a damn if the world hates him for doing so because from his standpoint it serves the greater good. Batman is willing to sacrifice his life or freedom to accomplish this objective.
Think of it as U.S. forces in a hostile nation. The U.S. military is clearly superior to the enemy. The U.S. military could quite literally turn the entire Middle East into a wasteland killing millions. This would wipe out all enemies, as well as millions of innocents. The U.S. military can't really utilize these tactics though for a litany of practical and humanitarian reasons.
Now think of the ISIS insurgent. This person believes the U.S. military to be a threat to his entire way of life, his culture, his civilization, his life and the lives of those he cares about. This person does not have the power, technology or capabilities of the U.S. military, but he also is not bound by the same humanitarian or practical restrictions. He can achieve what amounts to victories even if he ultimately sacrifices his own life for the greater good.
In the end, it isn't a perfect analogy because Superman can literally be killed by Batman with kryptonite and it is highly unlikely the United States will be destroyed by ISIS, but I think it works to give a practical frame of reference for why this god like creature can't just kill humans without consequences. Even Superman has to have quality of life. He can't be humanity's number one enemy. That would be a miserable existence even for him.