One of the most popular models for a flat Earth presumes the Earth to be a circular disc centred at the North Pole, and with Antarctica spanning the rim and providing some form of impassable barrier to simply travelling off the disc.
This raises the question of where the South Pole is. In such a disc model, there is no single South Pole – all points on the rim of the disc are equally far south. Yet people have travelled to a single geographic place that matches all of the physical requirements of being the South Pole of a spherical Earth:
1. People heading south always end up at this same spot, no matter which line of longitude they head south along.
2. At this place, the sun circles the horizon once per 24 hour period during the southern hemisphere summer, not setting until the autumn equinox, after which it circles below the horizon throughout the southern winter, only rising again at the spring equinox. This is exactly as expected for a physical South Pole on a spherical planet.
3. The place is directly underneath the point in the sky around which the southern stars appear to revolve, in a manner exactly analogous to the movement of the stars at the North Pole, but in the opposite rotational direction. The stars at the North Pole appear to rotate anticlockwise in the sky, while at the South Pole they rotate clockwise in the sky.
Furthermore, from this place, or areas around it, there are no directions in which one cannot travel. There is no visible edge of the disc, nor any impassable barrier to travel.
The same argument applies to the North Pole if the flat Earth is supposed to be a disc with the South Pole at its centre. And if the disc is some other configuration, then there will always be some point on the spherical Earth that ends up corresponding to all the points around the rim of the flat disc Earth – where it is straightforward to travel to that point on the spherical Earth but which is unreachable or should display bizarre properties (such as a rim or impassable barrier) on the flat Earth.
All of this is difficult to explain in a flat Earth model, but is a natural consequence of a spherical Earth.