Light bends to the left in positive refractive index materials, such as Earth's atmosphere. That shimmering you see over car hoods is caused by the fact that the photons cross a gradient of refractive indexes, and you'll note that the result is a smear of darkness surrounded by what appears to be blue air.
If you take a garden hose and point it up, you'll often note a spiral pattern to how the water is emitted from the hose, and how it comes back down to Earth. Light is doing the same thing - photons don't travel in straight lines.
On a sphere, light makes a series of curving arcs through the atmosphere, around the sphere. If the sphere is a dipole, the light will travel from ine pole to the other. The point is, all light on Earth does a curving orbit, and the result is a giant spiral across the surface.
Our eyes determine what we see - the position of the eyes relative to each other shapes the resulting image. By comparing the images received by the two eyes, a difference in perceived intensity can be discerned - this is the underlaying principle behind our perception of the horizon.
Birds, for example, see polarized light. What this means is that their eyes take note of the spiral of light - how the right-hand side gets flipped so it's now on the left. This allows them to reconstruct images that our eyes can't - they see what's beyond the horizon reflected in the sky above it.
To birds, the horizon looks further away. The shape of the Earth in this sense is very subjective, and using your eyes to deduce the curve of the Earth is very subjective and thus meaningless.
The stranger thing is that the concave Earth people have gone into the field, and substantiated their work. Given how subjective the horizon is, and how the convex Earth people report the same results but with the opposite sign, this would be the better avenue of inquiry.
