To study angels is to shed light on ourselves, especially those aspects of ourselves that have been put down in our secularized civilizations, our secularized educational systems, and even our secularized worship system. By secularization, I mean anything that sucks the awe out of things.
Fasting from words, fasting from a volume of speech, being willing to humbly accept the yoke of silence and quietude deprives the tongue of the mastery of our hearts and minds. The tongue is a very useful tool for the art of love and for the art of prayer, but it is also the means by which we afflict others and even our own selves so often. So it must be called into holy obedience.