Cuneiform tablets from the time of Hammurabi, recently discovered in the ruins of Nippur, indicate that the alphabet did not always begin with the eponymous letters "a" and "b".
The Babylonians, hellbent on doing everything in 60s, derived a 60-letter phonetic alphabet from their pictographic cuneiform alphabet. This, far from being overly complex, fitted the spoken Babylonian language perfectly. For example, there were 4 forms of the "q" sound which are utterly indistinguishable to Western ears.
There was apparently a bit of opposition to the laws of Hammurabi from traditionalists, religious nutters, and people suffering from lead poisoning. One such faction was a group which we will call the "Angry Sons of Tiamat" for reasons of brevity. In actual Babylonian,their name was a 37-word phrase, each word of which (by happenstance) happened to begin with one of the first 37 letters of the Babylonian alphabet, in order. This was a bit of a mouthful to say at one time, or even to write, and history recorded its first widespread use of an acronym.1
The Angry Sons of Tiamat were indeed quite angry, and held demonstrations, riots, 50-talent-a-plate fund-raisers, political conventions, square-dance competitions, bake sales, and the like to gain support. Their supporters grew to include a sizeable proportion of the Babylonian downtrodden, who weren't too happy about this "eye for an eye" thing not applying to when their own eyes were put out. Soon the 37-letter acronym sprouted on newly-daubed walls2 all over Babylon.
After one particularly violent and chaotic political convention/bake sale, Hammurabi decided he had had enough, and moved to suppress the Angry Sons. His troops faced stiff opposition. In the struggle, most of the city burned to the ground. Eventually the last Angry Son had his body thrown to the crocodiles in the Tigris and there was peace.
Just to show how serious he was about keeping the erstwhile Sons from coming back, Hammurabi decided upon one more reform: To make sure the hated acronym was never used again, he decreed that henceforth 36 of the 37 letters in the acronym would be removed permanently from the Bablyonian alphabet! He also decreed that all tablets with even one of these letters should be destroyed (requiring that his law code be re-written, obviously).
The exception was "iot" which was the only letter from the acronym in Hammurabi's own name. He nevertheless buried "iot" down in the remainder of the alphabet.3
The thirty-eighth letter was "alef" and the thirty-ninth was "bet". These became the new first two letters of the alphabet. The Babylonians passed it down to the Greeks who passed it on the the rest of the Western world. Note that the alphabets of the various Semitic languages also begin with these letters.
A faction of the Sons slipped away to Nippur and turned inward, writing mystical texts written in the full alphabet which were kept secret from the uninitiated. They survived until wiped out by the Arab conquest of Nippur in 622.4
1Perhaps the first name contrived for an acronym, who knows?
2The trouble with cuneiform is, you have to do your writing in wet clay. Now throw away those 5.25" diskettes.
3Hence, an "i" for an "i".
4The Sons' influence has not entirely gone away. Hammurabi's bureaucrats picked up the idea of the acronym from the Sons and passed it down through all the succeeding civilizations to the present day!