There are many contemporary articles on this subject, but without breaking the 20 year rule, it boils down to three major factors:
- The only game in town -- Atlanta proper has under a half-million people, but the larger metropolitan area had over five million people as of the 2010 census, and has only grown since then -- placing metro Atlanta firmly in the top 10 U.S. metropolitan areas by population. According to the 1950 U.S. census, the metro Atlanta area was the 23rd largest metro area in the country at that time, demographic trends since then have only acted to gradually move Atlana farther up in the ranking. The state of Georgia has since the early 19th century had a...distinct...form of municipal organization with a very large number of rather small counties, for the state's overall geographic size and population density. There are 159 counties in Georgia; for comparison, only Texas has more counties (254), and Texas has literally five time the land area and three times the population that Georgia does. All of this to say that calling Atlanta the "only the 38th most populous city" vastly unrepresents the relative demographic and economic importance of the Atlanta metro area in national and regional context. Which leads to the next point: Atlanta is a basically the only large city in it's region of the country, and the Harts-field Jackson Airport the only major airport for nearly a hundred miles in any direction. Many metros of similar size have two or three smaller airports -- for example, metro Boston, which is in population and area slightly smaller than metro Atlanta, has three international airports within 50 miles of the center of Boston: Logan, Manchester-Boston, and T. F. Green. But Atlanta has only the massive sprawling complex of Hartsfield-Jackson, which drives up the numbers of both flights and fliers by concentrating the entire metro areas passenger air traffic in a single massive airport, where in most American metros of similar size there are two or three airports between which the traffic is spread.
- Delta Air Lines -- Delta Airlines is one of the major U.S. legacy carriers, being founded in the mid-1920s, and in 1941 Delta moved it's headquarters and hub operations to Atlanta. Today Delta is the second-largest passenger airlines on Earth by number of passengers per annum, and Atlanta's Hartsfield-Jackson Airport is Delta's largest hub, by both flights and by passengers. In addition to being it's corporate headquarters and biggest passenger hub, Delta's operations center and primary maintenance base, Delta TechOps, is also headquartered in Atlanta, immdiately adjacent to the Hartsfield-Jackson Airport. So in addition to ordinary operations as a passenger and cargo hub, when a Delta airplane needs significant repairs or maintenance, it eventually gets sent to Atlanta. Delta TechOps is the largest MRO (Maintenance Repair and Operations) contractor in the United States, so quite a few smaller airlines send their planes to Atlanta for maintaince and upgrades as well. Historically, this means that since the early 1960s, Atlanta has been a regional if not national center for aerospace operations and logistics, so this isn't a new development.
- Location location location -- Atlanta is centrally located within the South Eastern United States, and nearly 80% of the U.S. population lives within a two-hour flight of Atlanta, which is one of the reasons Delta picked it as headquarters and hub back in the 1940s -- they could see where demographic trends were heading even then. The city of Atlanta is kind of in an odd place for a major city -- its not located on a coastline, nor on a navigable river or lake; rather, a town grew up around the location of Atlanta only starting in 1836, when it was chosen as the terminus of the Western and Atlantic Railroad, which eventually connected the Atlantic port city of Savannah with the U.S. Midwest, via the city of Chattanooga, which itself is an upstream point of navigation on the Tennessee River, which is a tributary of the Mississippi. So from it's very origin, the city of Atlanta exists only because it's at the intersection of two major railroad lines linking the Southern Piedmont, the southeastern Atlantic coast, and the Tennessee and Ohio river valleys. Through the later 19th and 20th centuries, Atlanta was the major rail hub of the south, and so became a center of commerce and industry as the the regional economies of the Atlantic Piedmont and Tennessee River Valley both gradually industrialized starting in the early 20th century. Because of it's good rail connections and booming industrial potential, the now-closed Fort McPherson just outside Atlanta proper was one of the major training and logistics hubs for the U.S. army for WWII through the ends of the Cold War.
I'm not an expert on Atlanta specifically, but the history of American urban regional economies is one of my many hobbies. SOURCES: This answer is drawn mainly from Frederick Allen's Atlanta Rising: The Invention of an International City, 1946-1996, with some supplementation from Eric Monkkonen's America Becomes Urban: The Development of U.S. Cities and Towns, 1780–1980, an excellent book that I cannot recommend highly enough for anyone whom wants to understand the history of urbanization, and the "rhetoric of development" in the United States more broadly.