Here's how I see it.
The general consensus is that the world is more or less spherical. There is a certain population, however, which believes that it is not. Rather, that it is more or less disk-shaped.
However, the people who believe that it is disk shaped really have no idea what shape it is. They just believe that it is *not spherical*. I don't know why they believe that it isn't generally a sphere, but the reasons aren't always the same. Conspiracy theory and alternative ideas about physics are offered as explanations for the reason that things are not as they appear.
However, if we are going to throw physics out the window - why settle for a disk-shaped earth? Why not a hyper-sphere, or some other unusual shape. Is earth really any more likely to be a flat disk than it is a hyper-sphere? If we disagree with physics as presented to us, then why settle for a physical system consistent with earth-as-a-disk when there are so many other options?