I had the same confusion reading the article.
IMO, the reall issue with callbacks is that they split your functions into two sets of uncompatible functions that cannot call each other -- the "async" functions with callbacks and the "sync" functions without them.
http://journal.stuffwithstuff.com/2015/02/01/what-color-is-y...
async/await mitigate this a bit because although the two kinds of functions are incompatible at least the syntax is the same.