Average airfare isn't a useful stat in this respect. What would be useful is comparing fares for individual routes over the years, which would tell a different story.
Average fares are skewed by low cost carriers entering the market.
The large carriers, created through mergers that should never have been allowed, have the most popular routes locked up through ownership of landing/takeoff slots and similar. On those routes, fares have substantially increased due to a lack of competition.
The low cost carriers business model is to fly new routes (to secondary airports if required) at low prices, often creating new demand (Breeze is a classic example of this).
The math is very straight forward if you consider what each group is doing in the market.
Average fares are skewed by low cost carriers entering the market.