When I began to study English in my high school (Moscow Institute of Applied Physics) I could not believe our teacher (or tutor?) that the English pronounce it as /aɪ/. I was all of shocked. In school I studied French and I always thought that all normal nations (at least European) pronounce it as /ɪ/. What is the origin of such crazy behavior of Englishmen?
The names of the English vowel letters used to be the same as all European languages:
That was before the Great Vowel Shift, as choster has explained.
Now they have different names, respectively
That's because the writing system didn't change, but the pronunciation of the language did.
English underwent a major and very rapid change in pronunciation around the 15th century known as the Great Vowel Shift, which explains in part why its spelling, pronunciation, and even names for letters of the alphabet vary from those of other European languages.
An English professor has posted a site including an audio demonstration of the shift at http://eweb.furman.edu/~mmenzer/gvs/ . According to Wikipedia the reason for the shift is unknown, but may be related to changes in society, such as English displacing French as the language of the aristocracy.