Why is there "Black English" but not "White English"?

African American Vernacular English is shortened to a less precise phrase "Black English". Also, Black English is used in a broader sense:

Black English is a term used for both dialects of English and English-based pidgins and creoles, and whose meaning depends considerably upon the context, and particularly the part of the world.

_{^{Source: http://en.wikipedia.org/wiki/Black_English}}

Also mentioned is AAVE is not regional anymore:

Although no longer region-specific, African American Vernacular English, which remains prevalent among African Americans, has a close relationship to Southern varieties of AmE and has greatly influenced everyday speech of many Americans.

_{^{Source: http://en.wikipedia.org/wiki/American_English}}

I see the usage of "White English" in some technical sources but I couldn't be sure what is actually meant by that. For example, there is the this explanation from Prof. John R. Rickford from Stanford University:

History of AAVE, exploring earlier examples of African American English, and its source in African languages, as well as the controversial question of its possible creole ancestry. Comparison with creole languages currently spoken in the Caribbean and off the S Carolina coast (Gullah) will be undertaken to shed light on this controversy. A more recent issue, which we will also explore, is whether AAVE is currently diverging from Standard English and White Vernacular English.

_{^{Source:http://web.stanford.edu/~rickford/AAVE.html}}

So, why is there a prevalent usage of Black English or Black English vernaculars but not White English (vernaculars)? (Or maybe not the usage of vernacular but the phrase itself... there are of course other dialects and sociolects spoken by White people or both White and Black)

For example, there are European Americans also but European American Vernacular English is mentioned in a very few sources. Could this be considered as White vernacular English by linguists in a broader sense? Is there any source that talks about this?

Of course this is related with the history of English and American English but maybe someone can shed a light on the specific topic. Also, I would like to keep the topic in linguistic sense (though it is related with races but within linguistic usages).

AAVE/Black English is an identifiable dialect; a hypothetical "White English" could only be identified and unified as being "other than Black English". There are large number of "White Englishes", several of them endemic to the United States, and each of them is identified separately. When considering grammar (which, in the linguistic sense means considerably more than mere word order and tense formation and so on), AAVE has unifying, distinguishing features, whether the speakers are in the originating areas, in the Loyalist diaspora, in Nova Scotia, in Africa (as the remnants of the Colonization) or in the Dominican Republic. It is essentially a slightly creolized hybrid of many English dialects (with a heavy Hiberno-English influence—neither speakers of Irish English nor Newfoundlanders find much of the grammar unfamiliar), and is different enough from other regional English creoles (such as Gullah/Geechee and the general Caribbean pattern) to deserve its own classification.

Relevant to your question is a conversation between the French linguist Mitsou Ronat and Noam Chomsky from 1976:

Ronat: I think it is very important for [William] Labov to show that the language of the ghetto has a grammar of its own, which is not defined as a collection of errors or infractions of standard English—

Chomsky: —But who could doubt that?  No linguist could possibly doubt that.

Ronat: ... Labov is primarily addressing teachers, pedagogues who do not recognize, in general, the legitimacy of the spoken language, and who, besides, have the ideological task of inculcating a feeling of inferiority in those who do not speak the standard dialect.

Chomsky: He is doing something very useful on the level of educational practice, in attempting to combat the prejudices of the society at large—and that is very good.  But on a linguistic level, this matter is evident and banal.... It is evident that the language of the ghettos is of the same order as that of the suburbs.  The study of Black English, from a linguistic point of view, is on a par with the study of Korean or of American Indian languages, or of the difference between the English of Cambridge, England, and Cambridge, Massachusetts.