I think what confuses people is the false, but intuitive fact that flying directly downwind will make up for the lost time of flying directly upwind the same distance. ie flying from A to B in headwind, then B to A downwind. This is of course a closed loop, and it will always be faster with no wind.
What matters here is the distance you have to fly through the air masses. Let’s say the wind moves perpendicular to the line A-B. Flying A-B-A with no wind correction will bring you downwind a distance exactly equal the wind velocity divided by the time you have used, point C. You then have to fly upwind that distance to get to A again, meaning you not only have to fly an extra distance (C-A), but you also have do it at a slower speed over ground.That higher speed over ground flying A-B-C won’t help you one bit.
Amazing work by lionel and alioth.
Now I know how fortunate I was to not get booted out of university, where I failed every maths exam but since I got 100% in electronics they could not get rid of me 
My answer was shorter and no less accurate. :)
