Quantas Airlines flight 28.

Santiago, Chile to Sydney, Australia. Direct, non-stop, twice per week. 13 hours travel time.

So, you're wrong. However, this does not prove or disprove earth being flat or spherical. It simply proves that you're wrong about intercontinental, southern hemisphere flights "have to go through northern hemisphere cities and take days".

Direct flights in the southern hemisphere are indeed rare, but that's primarily because the southern hemisphere has significantly less land mass and population than the northern hemisphere. There just isn't the demand for flights down there like there is between North America, Europe, and Asia.