Draco in Leather Pants/Analysis

There are many things to say about this trope:

1. All Girls Want Bad Boys.

Very simple, and the younger the Fan Girl, the truer it becomes. Villains often show the dominance, the rugged and wild physique, and the aloof Jerkass attitude that most teenage girls crave and that Heroes are much less likely to have. They wish to become the villain's Dark Mistress so they can feel protected and validated in their worth for having been able to inspire love in a monstrous man's heart. Being accepted by such a man means you're worthier than any other woman on earth.

2. The high status of female Love Martyrs among females (and, sometimes, among males).

Let's be honest, girls love to drown themselves in a sea of hormonal emotions. Most Fan Fictions featuring a Draco in Leather Pants often make him a Bastard Boyfriend who turns into a Reformed Rake in the end, through The Power of Love. Many teenage girls want be on an emotional roller-coaster and feel constant insecurity about whether or not their boyfriend loves them. It makes them feel alive and gives them the feeling that they have a purpose in life. Being strong enough to love a man forever, no matter what he puts you through or what he does to other people makes you a respectable and admirable woman, according to many teenage girls. Hence the glorification of Love Martyrdom, which is what most villains guarantee.

3. Reverberation of high status.

Villains are often ambitious. Since most of them often become kings, emperors, or have some form of authority, girls dream about being the respected dark queen at their side, whose high status ensures that no one will ever be disrespectful to her or disobey any order she may give as a the Dark Lord's lady. In other words, the freedom of being a bitch and not getting any flack for it. House proves that many men like being jerks and get away with it. Women are no different.

4. Evil Is Sexy.

It's true for men. Femme Fatales and Vamps are often considered "hot" by Fan Boys. While the heroine may look pretty, she doesn't ooze sexuality like villainesses tend to do, since, as we all know, a sexually active woman is not wife-material. Since this is inverted for males, the sexiness male villains ooze is often inherent and switches on many girls' desire to be dominated and literally owned by a bad man. Love Martyrdom often involves Sex Martyrdom and other kinds of unsavory things. All of this is nullified if the villain is physically unattractive, though.

5. I Can Change Him.

The inverse of #2, in this case it's the feeling that the girl's (or guys as well) love is capable of changing the Draco.

It is possibly a real-life example of All Girls Want Bad Boys (most victims of this trope are male). Characters of this type are also often prime repositories for Fetish Fuel, so softening their darker aspects may, in some cases, be a fan's self-justification for her own Perverse Sexual Lust.
It's also true that many villains (especially nowadays) come with some story attached that does make them seem more sympathetic. This can sometimes cause fans to zero in and forget that the characters are still supposed to be villains.
In fairness, more than a few authors have written morally ambiguous characters, then acted surprised when sections of a fandom embraced them as heroic. The personal nature of morality means that actions one person finds to be equatable to dog-kicking will seem perfectly justified, even pragmatic, to another, especially if it's of the Designated Evil variety. This is especially common with the Magnificent Bastard and the Designated Villain. This can be especially true if the setting is a Crapsack World or World Half Empty: in a state of moral ambiguity, if the heroes are not good, and the bystanders are not innocent, audiences will naturally root for the coolest character.
Some villain archetypes, such as the Smug Snake (because of their off-puttingly arrogant personality), female villains (they may even be hated for exactly the same actions), AntiHeroes, AntiVillains, and the Complete Monster (because of the severity of their evil deeds) are rarely susceptible to this. But it can still happen.
And sometimes, it simply proves that some girls (and some guys...) will completely ignore someone's horrid deeds and personalty, simply if they find them sexually attractive.
Many villains also imply with their actions that they are physically strong/healthy/fit (at least strong enough to become a serious problem for the heroes) and physical strength and the possibility of becoming an alpha male is always a trait which makes people physically attractive in a biological way.