You want to know more about me? Aww, aren't you the sweetest thing ever! After all, I know everything about you...
A possible origin of the Yandere tropeYandere may have emerged as a deconstruction of the Yamato Nadeshiko archetype: an eternally serene woman who always puts the needs of her family and husband before her own. A yandere is all of this driven to the logical extreme and then examined realistically: a sentient individual put in such a position would invariably experience enormous emotional and mental strain. Sooner or later, she would snap, even at the slightest provocation. Ironically, it is this realistic take that makes a yandere so endearing to the audiences, often even more so than the traditional Yamato Nadeshiko. (Granted, there are realistically a wide range of possible responses to stress other than going Axe-Crazy, but this one is definitely more entertaining to watch.) Compare with the Violently Protective Girlfriend who can become Axe-Crazy when the love interest is in danger but is otherwise much more stable mentally. See also Living Emotional Crutch for a reason why she goes from affectionate to murderous.
Why Yandere can be perceived as attractive
- Someone who is crazy for you is someone who is crazy for you.
Interestingly, these types of characters can still be perceived as attractive if they can build up enough tragic audience sympathy, despite the argument that many originally become popular by being subversions of wishy-washy female characters until the fandom ended up loving them in the typical way (what sweethearts!). Sometimes this can play out in story, if the Love Interest ever starts to rethink his relationship with this girl, she might threaten to harm him or herself if he ever leaves her. This threat might be explicit, but often is more subtle.
The Yandere can be attractive because of the simple fact that they are insanely infatuated with the one they love. There is no issue of infidelity on the Yandere's part. They would never cheat, emotionally or physically, on the one they love. For one who has been cheated on, this can be a very endearing trait.
Also worth noting is that the Yandere is typically a (physically) beautiful or attractive person and they are typically of above average intelligence or even genius level intellect. Otherwise they would simply be an Abhorrent Admirer. In this case, who wouldn't want a supermodel whose only thought is of you? Or an intellectually interesting person whom you can FINALLY have an intelligent and stimulating discussion with? A person whom (individually or a combination of the two) can provide a financially stable life?
How would you like someone who cares about YOUR needs and YOUR interests over their own? These attractive traits seem good. Until they begin deciding that you don't know what is best for you... but THEY do. Maybe you do need some improvement but the method of improvement is up to them and it can become quite unpleasant or deadly.
And of course, there exists the idea of "I can change them." The idea that, somehow, your actions or your love with steer them away from their murderous ways. You can watch any episode of COPS that involves a domestic dispute, several episodes of Maury or The Jerry Springer Show to see this mentality come into play. In this case, the Yandere doesn't need love, and the action that should be taken is to get them psychiatric help - because they are mentally ill.
There is a guide how to win a yandere and live with her. Be warned, once she falls for you (or rather, you for her) there is no turning back. God help you if you get stuck in a Psychotic Love Triangle. We all know how those go down.
The Trouble with Yanderes
A main problem with a Yandere is that a poorly-written Yandere can easily become The Scrappy. As outlandish as the trope can be, Yanderes can still be likable as long as they have elements of sympathy with them, but alas, there are a few that lack that key redemptive trait. A Yandere written to be unlikable is more than likely to be a villain of some caliber, planning to cause harm to a more level-headed character in a fit of blind fury simply because their dream relationship fell apart. Another bad sign for a Yandere is if he or she suffers from Erotomania, and delusionally believes that the person they love is in love with them when in reality, the person is either indifferent or wants nothing to do with them. Unrequited Yandere attraction never ends well, and can be very ugly if the Yandere goes off the deep end.
If you don't read the unabridged version I wrote especially for you, I'll gouge your eyes so you will never look at another trope!... Okay~?