Barry Powell should have listened to his grammar school teacher. It was the Phoenicians who invented the alphabet.
The Phoenician script was strictly consonantal. Vowels were not represented, and the reader was required to supply them from his or her knowledge of the language. This system worked reasonably well for Phoenician, since in that language there are no words that begin with vowels. But in Greek many words do begin with vowels. So when the Greeks adopted—and adapted—the Phoenician script, they needed to add new signs to represent vowels. The result was a significant advance in sophistication and precision—a giant step forward in the evolution of the alphabet.
Powell doesn’t agree. He considers this step the creation, rather than simply an improvement, of the alphabet. In his view, the Phoenicians had no alphabet. Here he follows I.J. Gelb’s old notion that the so-called Phoenician alphabet was not an alphabet at all but a syllabary, in which each sign represented a consonant followed by any vowel (or no vowel)—thus the b-sign could be read as ba, bi, bu, and so on (or simply as b).