58) “The Royal Belgian Geographical Society in their “Expedition Antarctique Belge,” recorded that during the most severe part of the Antarctic winter, from 71 degrees South latitude onwards, the sun sets on May 17th and is not seen above the horizon again until July 21st! This is completely at odds with the ball-Earth theory, but easily explained by the flat-Earth model. The Midnight Sun is seen from high altitudes in extreme Northern latitudes during Arctic summer because the Sun, at its inner-most cycle, is circling tightly enough around the polar center that it remains visible above the horizon for someone at such a vantage point. Likewise, in extreme Southern latitudes during Arctic summer, the Sun completely disappears from view for over 2 months because there at the Northern Tropic, at the inner-most arc of its boomerang journey, the Sun is circling the Northern center too tightly to be seen from the Southern circumference.”

A Belgian expedition found that the sun sets on May 17th and rises only the 21th of July. This was at 71 degrees south latitude. Dubay asserts that this is 'completely at odds' with the sensible theory, without explaining why. You know, like in the rest of his entire article.

Let's first establish something. Dubay say it was from 71 degrees south latitude onwards, but this is not true. The actual expedition got stuck/trapped in the Bellinghausen Sea, and had to remain there for the entire winter. As a result, they were stuck at that latitude, having frozen the vessel in ice for the winter. As this is within the Antarctic circle, it is not at all at odds with the sensible theory. Indeed, the Antarctic circle is defined as the latitude closest to the equator for which the sun can stay up for longer than 24 hours (or, indeed, down). 

Their assertions depend, as usual, on not showing that anything is actually true.

In particular, it is noteworthy that they don't define the Horizon on their flat earth model.

Winter solstice -> polar night. When? December 21 in the north, June 20 in the south (as of today). 

What these Belgian explorers observed, was a polar night! And it's not at odds, it's completely in sync with the ball-earth model.