It's because people are subconsciously scared when they find out that their elected leaders are as human and full of vice as they are; society elects those they are deluded into thinking are saints and can do all the conscientious thinking for them so they don't have to. Then when something scandalous leaks, they like to get on their high horse (forgetting that they voted for that person in the first place) so they can continue to ignore their own faults.
Because we have to chase him. Because he's the hero Gotham deserves, but not the one it needs right now. So we'll hunt him. Because he can take it. Because he's not our hero. He's a silent guardian, a watchful protector. A dark knight.