I'm sure anyone reading this blog is familiar with the Queen's English Society and their mission to protect English from the rampaging hordes of young people and Americans. I didn't write about it because Stan Carey at Sentence First said everything that needed to be said. But recently Gabe at Motivated Grammar addressed a specific complaint the QES makes, and I became interested in doing the same (or biting his style, as the kids say).
The QES objects to either pronounced with /i/ (the "ee" sound) instead of /aɪ/ (the "eye" sound). Their reasoning is twofold:
1. The /aɪ/ pronunciation is "upper-class" and "cultured", and changed to /i/ in the 50s "probably" under American influence.
2. "many words in English come from some form of Old German", and in German the letter combination ei is pronounced /aɪ/, so therefore in English words of Germanic origin, ei should be pronounced /aɪ/ as well.
Regarding point 1: I'm not sure how the QES knows how and when the pronunciation changed. For the record, both pronunciations of either are standard. The /i/ pronunciation is usual in American English, while /aɪ/ is more common in British English. However, /aɪ/ is found in the speech of "well-educated speakers in urban areas of the Northeast" US. I find it weird that pronouncing a word with a high front unrounded vowel as opposed to a falling diphthong is seen as a "regrettable" infiltration.
Regarding point 2: there are several problems with this. From one point of view it is true that many English words are derived from a form of "Old German", but this in turn means that many German words are derived from a form of Old English. The ancester of both languages is a putative language called Proto-Germanic, so Proto-Germanic is a very old form of German, but it's also a very old form of English. So why don't the Germans look to English to find out how to pronounce their words?
Next, the claim that ei should be /aɪ/ in English because that's how it's pronounced in German looks like a form of the etymological fallacy: the belief that we need to look to another language to determine what makes correct English.
Finally, the argument that the /aɪ/ pronunciation is correct because of the word's Germanic history doesn't make sense because historically, the /aɪ/ pronunciation is wrong. Either developed from Old English ǣġhwæðer, a combination of ā "always" plus ġehwæðer "each of two" (modern whether). It was contracted to ǣgðer, then later spelled either - so it's the development of the initial ǣ that concerns us here. Old English ǣ was usually pronounced /æː/, and this generally became Middle English /ɛː/ which became Modern English /i/. For instance, Old English tǣcan with /æː/ became Middle English teche which became Modern English teach with /i/. So it seems that the etymologically correct pronuncation of either is with /i/.
The OED notes that the /aɪ/ pronunciation is "not in accordance with the analogies of standard Eng[lish]" (I'm not even sure what that means, actually) but that it is "in London somewhat more prevalent in educated speech" than the /i/ pronunciation.
Summary: The /aɪ/ pronunciation still seems common in British English, but even if it isn't nothing important has been lost, and German spelling is irrelevant to English pronunciation.
The American Heritage Book of English Usage (1996).
 Oxford English Dictionary, either.
Millward, A Biography of the English Language (1988), p. 131.