Actual Flight Paths

If you study the map above, you will notice that the routes that airliners take in order to travel from one destination in the Southern Hemisphere to another destination within the Southern Hemisphere, make absolutely no sense on a spherical earth.  Why would airliners go out of the way to double and often triple their distance flown, by choosing a route that takes them into the Northern Hemisphere, land, and take off again toward the Southern Hemisphere. In this day and age of competitive pricing, this type of route makes no sense whatsoever.