44) “If Earth was a ball, and Antarctica was too cold to fly over, the only logical way to fly from Sydney to Santiago would be a straight shot over the Pacific staying in the Southern hemisphere the entire way. Re-fueling could be done in New Zealand or other Southern hemisphere destinations along the way if absolutely necessary. In actual fact, however, Santiago-Sydney flights go into the Northern hemisphere making stop-overs at LAX and other North American airports before continuing back down to the Southern hemisphere. Such ridiculously wayward detours make no sense on the globe but make perfect sense and form nearly straight lines when shown on a flat Earth map.”
 

See Point 43 above. Many of the same factors apply here.

“The logical way to fly from Sydney to Santiago would still be a great circle. So no, it wouldn't be a straight line. Here's the route on a Mercator Projection.

If you don't know what map projections are - and I should've raised this point before - now is the time to learn. I'll refer you to a neat webcomic to get you started.In the meantime, here's the Great Circle route from Sydney to Santiago (Chile). 

I'm not sure about their detours - not only is there apparently a direct route now, there's always been flights with a small stop in New Zealand [traveller.com]:

LAN operates daily one-stop flights between Sydney and Santiago via Auckland, providing onward connections to over 115 destinations in South America.

So they don't actually make that detour. If you look at their image to the left, you see how much of a `detour' they would make on a flat earth map.” 

Thanks, Daimonie