The word inauguration comes from the root  augur which is defined as a verb. It means to predict from an omen. anticipate, call, forebode, foretell, predict, prognosticate, promise. make a prediction about, tell in advance. 
In ancient Rome, the guys love Roman stuff. Augur was a noun, a name  for a religious official who observed natural signs, especially the behavior of birds, interpreting these as an indication of divine approval or disapproval of a proposed action. Inaugurate is very pagan stuff.