“But this is Gotham City. This is our city. And when hell is unleashed, we don’t run and hide, we stand up. And there’s a symbol, a symbol we all know stands for what we can do. What we are capable of. Tonight needs more than just one hero. It needs a city. It needs all of us. Tonight we all need to do what he does for us every night. Tonight we all need to be Batman.”
-Jim Gordon, Batman Eternal #52
Batman is a symbol, an idea, not one singular person or a specific gender. That’s why Batman is eternal.