The idea of an alphabet is usually ascribed to the Phoenicians. At the least they had the earliest one that we know of, and the others that we know of (including the Greek, Roman and eventually our own) developed from theirs.

Compare and contrast to alternate forms of writing such as Egyptian hieroglyphs. The key idea that writing should represent how you would say the word is, as best we know, a fundamental advance that is due to the Phoenicians. The point is to make it easier to translate spoken fluency into literacy.

In short our alphabet descends from the recognition of the value of making literacy possible through phonics by the Phoenicians.

This is why I ascribe the origins of phonics as a teaching method to the Phoenicians. Any similarity of names and Greek word roots may or may not be entirely a coincidence.

Cheers,
Ben