You've not received an answer to your query because you posted in Flat Earth Debate. No one wants to debate this because it's asked all the time. Use the search function if you want to see our answers, post it in FE Q&A if you want answers, or come up with something interesting to debate if you want a debate.
Fine. After searching and reading a bit in different threads related to the issue, I have found two stances assumed by the FErs:
1. There is no correct FE map. Sigh... Then why don't you all simply remove this polar projection from your site, as it is pretty obviously flawed?
2. There exists a strange, quasi-relativistic effect called "associative time dilation", where being in flight causes the time flow in the following ways:
a) to you, on the plane, it looks like the flight takes X time
b) to people on the ground, it also looks like your flight takes X time
c) time somehow flows
faster for the people on the plane - why doesn't it then look like the flight takes more time for the person flying? I have no idea.
d) reality somehow "catches up" itself again after landing, so both sides experience the same flight time, while in fact(I have no idea what this phrase actually would mean here) it took longer than actually perceived by anyone.
First of all, I have no idea how this second thing would work to give an effect of planes magically speeding up while still going a regular speed, and second, why such a description would even explain the observed effect of planes travelling similar distances on both sides of the equator.
On a side-note, feel free to guess who came up with such an elaborate explanation. And it would be nice if Pongo replied if this is what he considers a valid answer, and if so - if he could explain why does it seem to work much stronger when flying along the "edge", closer to it, and not in other places or directions.
Oh, and another explanation - by the same creator - is that on the southern hemisphere, there live some creatures which help travel at times fitting a RE.