The federal Civil Aeronautics Board (CAB) had regulated all domestic air transport as a public utility, setting fares, routes, and schedules. The CAB promoted air travel, for instance by generally attempting to hold fares down in the short-haul market, to be subsidized by higher fares in the long-haul market. The CAB also was obliged to ensure that the airlines had a reasonable rate of return.
Could you imagine what fares would be like today if this administration was running the show and had to guarantee a reasonable rate of return?
Additionally, it was virutally impossible for any carrier to start flying in the U.S. Even Southwest Airlines which started in 1971 could only fly within the state of Texas before deregulation. (The CAB could only regulate interstate flights not intrastate flights.)
Both Democrats and Republicans were behind the move to deregulate. Teddy Kennedy was one of the strong voices for deregulation even though the original idea came from Nixon.
Whether or not you think the aftermath of deregulation is good, that's a different story.
Sorry to say that deregulation had already begun way before Reagan took office--although I would love to find something else to blame him for. Oh yeah, he didn't help any by firing the Air Traffic Controllers.
I also remember the days when to get a cheaper fare, you had to fly after 9 PM.