While every girl grows up with the idea of finding her forever Prince Charming, there is no dispute in the appeal of the bonafide bad boy. The charm of the bad boy is irresistible to some with all its bravado and boldness.
Females respond to emotions rather than logic. Men have more of a masculine energy, centering on logic and reasoning. Therefore, women are more drawn to situations in which stimulate emotions. This results in the reasoning in why women don't necessarily crave a "nice boy" who opens your door, pays for your meal, and politely kisses you goodnight at your doorstop. While long term this is what most women want, this too one-dimensional personality just won't cut it for the inner feminine energy yearning for some type of strong evoked emotion. The bad boy entertains the inner feminine far more by unleashing a full range of emotions which is part of a natural, stronger attraction.
We don't want what's good for us. What's bad for us feels good. For the female, she is well aware that she shouldn't engage, but like that second slice of decadent pie, how can she resist? She is well aware he will be bad for her, but knowing he is the wrong choice in a way makes her want him even more. Rebellion and a bit of unpredictability helps her feel a sense of freedom as she is able to release stress and adrenaline. Add in the dominance and confidence trait and you've got yourself one hard-to-get emotional attraction and chase.
There is no dispute women have a rescuing nature about them. We are nurturing fixers and when we see a bad boy, our "must fix" part of the brain lights up. It becomes our new adventure and challenge to reform this bad boy into a good boy as if he is our newest project. This inflates our ego when she feels as if she has the power to change him into her Prince Charming and thus, the man will feel indebted to her and therefore, maintain a sense of security and not leave. This is almost detrimental to the female as unfortunately they won't change unless they have the personal motivation to.