Er... Author has it backwards. The question isn't "Why ABC?" It's "Why not some other order?"

The "ABC" ordering probably won for the same reason as the "QWERTY" layout won in the U.S: because that's what everyone learned with, so that's what everyone teaches with.

There's going to be some "canonical" order for something like an alphabet, and whatever order that was, we'd be sitting here today asking "Why this order?" If there is no obviously better order, then this one's simply as likely as any other.