As you can tell from the Petite Planète logo, I am quite familiar with maps that have North and South switched around. The problem is that this guy picked a map that does not have the equator in the middle.
While every map, as a two-dimensional representation of something three-dimensional, has to distort somewhere, the equator is simply a line of splitting the Earth into a top and bottom half -- or, as Wikipedia puts it:
... it is an imaginary line on the Earth's surface equidistant from the North Pole and South Pole that divides the Earth into a Northern Hemisphere and a Southern Hemisphere.
There are various ways of stretching the polar extremes to fill up two-dimensional maps, but moving the equator towards the South Pole does not help in any case; if anything, it causes another completely unnecessary problem by making the northern hemisphere look much larger than the southern hemisphere.
My favorite representation is the Peters map, which stretches things so that land mass is roughly equivalent. If you are looking at a map that seems to suggest that Greenland is roughly the size of South America, you are not looking at a Peters map (map source: Nasa).