Why? Well, first off, Batman gets a whole arc by the end of Batman v. Superman. He starts off as an obsessive murderer, paranoid that Superman is an unforgiving alien who's just going to cause more damage. We see the costume of a deceased Robin in the Batcave, so we know that his closets are nothing but capes and skeletons. But by the end, he accepts Superman and teams up with him, proving that he can trust and dance and live and laugh again. On the other hand, Superman starts the film wondering why everyone hates him, and the only progression he gets is learning that some people might not hate him.
Rather than using Superman's death to prompt Batman to team up with other people (something that we already know that he's capable of doing), use Batman's death to prompt Superman to actually be a selfless hero. Batman's a jacked fascist weirdo with a dozen machine guns in his car, and even he's able to put his differences with others aside to fight a greater problem. If that guy is able to stop worrying and make a positive change, then Superman should definitely be able to get over a bunch of puny humans calling him mean names. Then you make Justice League about the quest to revive Batman, because for real, I'm not sure that the rest of the League knows how to use Google.