Yeah, it makes sense. I'm hopellessly pre-Crisis, I know. You must pity me. But I never could buy into the Batman/Superman split that came in the mid-1980s. It always seemed ridiculously over-emotional and not the way two adult heroes should act. But that was thirty years ago. Are we really stuck at the same place with these guys? All the other iterations of Batman and Superman never lasted that long. You would hope that characters move past one emotional state and change and grow.
It seems like the people promoting this dichotomy are hung up on the symbolism--Batman is darkness, the night, the human; Superman is brightness, the day, the super-human--but that treats characters as stock images and not as fully rounded individuals. When you look at Bruce and Clark as human beings, there should be more that unites them than divides them. But then there's this strong collective of readers who think there is no Bruce Wayne (he died with his parents) and there is only Batman. And they also claim there's no Superman (that's just a mask) and there is only Clark Kent. So, I guess, it's easy to force this dichotomy on the two heroes when you frame them as such total opposites.
I don't see them that way. I see them as complex characters. Bruce Wayne didn't die--otherwise Batman would be suprahuman, not anchored in any human emotion and totally overtaken by symbolism--but we know that he has relationships, feelings. There has to be a part of Bruce Wayne that persists and wasn't killed by the Batman inside him. As a real person, Bruce loved his parents and feels their loss. Superman and Clark Kent are two sides of the same person--Kal-El who lost his home, his parents at an early age--and who formed a bond with his adopted parents (who may or may not be dead, continuity depending). Both Bruce and Clark are damaged individuals, with a strong sense of justice, who want to prevent others from experiencing the pain they've endured. They both feel like outcasts in society and hunger to have emotional connection with others, yet are fearful of those connections, because they could lose everyone they love and suffer more pain and loss as a result.
Bruce and Clark are highly intelligent and have the abilities to acquire information on the other. They can't keep secrets from one another. Clark will know everything there is to know about Batman and Bruce will discover everything there is to know about Superman. That might make them fearful of each other, but they can only hide for so long. They will find each other out. And with that has come honesty and a recognition of the other in themselves. Superman is not so bright as the world believes and Batman is not so dark--and it's Clark and Bruce who are equipped to see those nuances in each other. That makes them brothers. The two heroes who can understand one another best, because no one else in the DC universe is at their level.
They've been through wars together, they have each other's back. Superman knows that the hero he wants by his side in a fight is the Batman, because Batman never gives up. And Batman knows that Superman is solid, a bulwark against any and all attacks.
It's like with the Beatles. The only other person who could understand what it was like to be a Beatle was another Beatle. Only they had that rare experience. There are only two heroes who are the World's Finest, Superman and Batman. That connects them in ways that no other DC heroes can be connected. And they both had mothers named Martha.