Why be smart if one is a beautiful girl? They can just sit back and be lazy. All they really need to know is home ec. and that's about it: the rest of life is a free pass due to their looks.
Being smart is almost invariably for the ugly/undesirable. They're the only ones who have TIME to learn anything.
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.