Here's a mishmash of explanations I either believe personally or have heard others put forth. Obviously not all the reasons hold true for all Asian girls; the preference for white guys probably derives from some combination of some subset of these factors.
Assimilation into Western society. Having grown up in a Western society, Asian-American girls sometimes identify more with "white" culture (defined by things like http://stuffwhitepeoplelike.com/) than with Asian culture -- as such, referred to as "bananas", for being yellow on the outside but white on the inside. A girl who perceives the world from a Western point of view is naturally drawn to others who she perceives to belong to Western society. Unfortunately, a whitewashed Asian guy still looks Asian.
Perception of physical attractiveness, influenced by Western standards of beauty. Attractiveness is a societal construct, and most of society today (including modernizing Asian society) is fixated on Western standards of beauty. Consider the football player archetype: white, tall, rugged, chiseled face. This image matches up pretty well with some of the more popular male celebrities in entertainment: Brad Pitt, Justin Timberlake, Tom Brady. By contrast, there aren't really any icons of Asian guy hotness in Western media.
Greater confidence of white guys as compared to Asian guys. See Quora User's answer on How do Asian guys feel about Asian women dating white guys? for a great discussion on the incubation of nerdy, shy Asian boys in American society over the last couple of decades. Girls are attracted to guys who are confident and sure of themselves -- not so much guys who are very soft-spoken and timid, even if they are "nice guys". Refer to the aphorism "nice guys finish last"...
Rebellion against traditional culture and/or a desire to seek something new and different. Many people desire to be nonconformist or to break away from tradition. It's completely understandable that an Asian girl might be tired of familial and cultural traditions, especially if they seem to her rather outdated in the modern world; and she would thus seek something novel and exciting in a relationship with a non-Asian.
Rebellion against over-parenting ("helicopter parenting"). In light of Amy Chua's highly controversial op-ed in the WSJ, this note rings especially clear. Teenage rebellion is nothing new but Asian over-parenting is well-known to be especially onerous and rebellion-inducing. It's not clear why this might apply more to girls than to guys but maybe it's that Asian girls have an easier time dating white guys (white guys are more receptive) and also that it's a slightly bigger statement of rebellion for the girl, as there is more a sense of the girl leaving her family to join that of her husband, a non-Asian family, if the relationship reaches that stage.
Potential for cute babies. I think there is general consensus that white/Asian mixed-race people are on average more attractive. They have larger eyes and more pronounced noses than pure Asians, but these "white" features are softened by the Asian heritage. Hapa kids are pretty adorable.
Ability to date someone a little further up the attractiveness scale. I've heard some people say that white guys don't know which Asian girls are actually attractive amongst Asians and are by consequence less discerning in their taste. If that's the case, then a less attractive Asian girl (by Asian standards) would be able to score a relatively more attractive white boyfriend or husband.