Many versions of Batman have a strict "no killing" rule, which is exactly the kind of intuition the Trolley Problem is attacking. Why is it different to actively kill someone vs passively letting five people die? In particular, Batman's version seems to be a sort of "honor code", which something close to a moral system, but it is entirely inward looking. In other words, fulfilling the honor system doesn't do good for the world, it elevates the status of the honorable man. In a sense it's the worst possible way to answer a moral question, "I want to kill the five people because I personally would lose something (my honor)".
Also its pretty showy to dress up as a bat. One might even call him a weirdo.
