To start this out, this is my own personal findings about Batman/Bruce Wayne's character. Michael Keaton, Christian Bale and Ben Affleck have portrayed Batman well, but they lack the understanding of the character. So, this could be easily stated that Bruce Wayne is a troubled soul, who runs around using his billions of dollars trying to save a city dressed as a Bat-man, but I find it's deeper than that.
First, why he fights crime. Because his parents and only family were killed in front of him, he feels guilty, like he could have done something. He doesn't know how to handle death, because he was a child when his parents were murdered and for a child, that is devastating. He simply can't handle the thought of losing the people he loves, so he latched on to Alfred for comfort. He is, was and will always be troubled with death, because, like I've stated, he doesn't know how to handle it (as seen with Jason Todd).
Second, why Bob Kane chose a bat. Before you say, "Because bats are what scared Bruce as a child ," you have to think about what bats represent. According to Native American culture, bats are highly social, have strong family ties, they're nurturers, and motherly figures are important to them. Bats live in caves, which is also like exploring the underworld, and bats also touch on inner demons. So, Bruce has quite a few character traits quite like a bat. He holds to his mother dearly, remembering her pearl necklace. He has his own inner demons that he covers with his fear of bats, and he influenced his new family to his alter ego, even if he doesn't mean to.
Thirdly and finally, why he doesn't kill, normally anyway. Bruce won't kill people intentionally, but that doesn't mean he won't beat them to a bloody pulp. He is afraid of death, and won't kill criminals because he wants them to share his fears of death and of, bats. If the criminals die in a car wreck, gunfire, and etc., it seemingly doesn't matter much to him. He won't kill joker because, whether he'd admit it or not, he relates to joker. The same with scarecrow, two-face, penguin, etc.
These are the reasons actors have a hard time portraying the Dark Knight, because it is difficult to put yourself in such a pair of complex shoes. Batman has become a typical, cliched superhero who has been represented shallowly throughout the years. Even actors as great as Michael Keaton, Christian Bale, and Ben Affleck have still somewhat failed at portraying the character. Those three have been the greatest, even though Affleck still needs to prove his iteration of batman through the Justice League and solo films. Even still, the perfect batman/dark knight/and Bruce Wayne still are yet to be seen in live action cinema. Mabey one day we'll get the Kevin Conroy of the live action universe, but, as I've said, it remains to be seen.