The "Flat Earth Society" refers to an ideology that the planet Earth is not a sphere, but rather a flat disc. It was originally founded as the "Universal Zetetic Society" by Samuel Rowbotham in the 19th century, whom published several issues of a magazine titled "The Earth Not a Globe Review". While most people who claim to believe in Flat Earth are trolls or otherwise non-serious, there are individuals who take it seriously; usually motivated by pseudoscience or religious beliefs Through the use of social media, flat Earth theories have been increasingly "supported" by individuals who are otherwise unaffiliated with any large flat Earth organization or group.
Arguments[]
These are some of the common flat Earth arguments that are prevalent amongst the believers of the theory, along with a rebuttal.
"You can't see curvature"[]
A common argument by Flat-Earthers is that you cannot see the curvature of the Earth. The Earth curves at 8 inches per mile squared, due to Pythagoras calculations using the radius of the Earth, this means the objects start disappearing behind the curvature every 8 inches per squared mile. Example: 20 miles away would have a curvature of 20^2 miles * 8 inches / 12 inches = 267 feet of curvature. Using a common camera, the objects should be hidden by the curvature of the Earth if the size of the object is less than 267 feet, and you are at ground level.
Rebuttal[]
Height does play a major role in your visibility as well as refraction. The higher you are, the more you see; while the lower you are, the less you see. At ground level, it is possible to see objects further away then the curvature allows, due to refraction. Light can refract and bend inside the same medium depending on the temperature difference of the air along the distance you are looking. Hence, if looking over water, there will be more humidity and more precipitation which would cause more refraction compared to on land.
There are no photos of the Earth[]
Another common argument from Flat-Earthers is the fact that there are no "real" photos of the Earth. This was due to a NASA artist saying "it is photoshopped because it has to be".
Rebuttal[]

The Blue Marble photograph - Earth as seen by Apollo 17 in 1972
This argument is blatantly false; there are many photos taken of the Earth, with the most famous one probably being the "The Blue Marble" (pictured right). Typically, they will argue that this is fake, simply because of that NASA artist. However, they forget to realize that the data was collected from various space probes and combined into an image. This is because Earth is so big: probes stay in earth's orbital distance so they do not continuously fly into infinite space. Those that are made to go into infinite space are able to take pictures you see on the right.
Why is travel to Antarctica banned?[]
This argument is used by several flat Earthers to prove that the government (or NASA) is hiding something, e.g. the fact that Antarctica "surrounds" the Earth. Since water always finds it's level, they believe it is contained on Earth and Antarctica is the barrier. This is mainly due to their belief that water cannot curve and stick to a ball... and yes they do not believe that gravity exists.
Rebuttal[]
Travel is not banned to Antarctica. While there are some rules, anyone can visit Antarctica if they please. There are many commercial cruise ships that will travel to Antarctica.
It is not allowed for independent travel due to harsh weather conditions and scientific research. Antarctica is the coldest place on Earth, this allows scientists to test various equipment and chemical bonding. Furthermore, the simulation of a harsh environment is beneficial for animal trials during the experimentation with chemicals in order to analyze their potential improvements.
Due to the south pole being having a constant positive magnetic field, scientists are able to study the effects of anti-magnetic radiation from beneath the snow: This would otherwise cause severe health risks if exposed for a short period of time. On average, the radiation causes serious injury to internal organs after 3 hours of exposure. Anti-magnetic radiation protection suits for these scientists is constantly improving, to protect the public, once these suits are capable of allowing for at least up to 24 hours of protection in case of emergencies, it is better safe then sorry.
Gravity doesn't exist (Universal Acceleration theory)[]
Another common argument that the "Earth" does not move at all by the majority of Flat-Earthers.
The cause of objects falling is usually simply attributed to "density".
Rebuttal[]
Einstein first made the claim that Gravity is not a force, however, it's simply the best model we have to explain our universe.
The reason why it cannot be density is due to our space observations. Density does not account for orbits nor does it explain how objects act in space or on other planets. Gravitational force is observable and is proven fact with the help of technology we have today.
Flat Earthers simply take Einstein's word that, "gravity is not a force", and forget to do their research regarding the countless articles and studies for gravity. Most do not accept the Cavendish experiment, but that is simply illogical due to the number of times it has been repeated. Not to mention other experiments of gravitational waves, and of course there are always some Flat-Earther's that call it "fake"...
Summary
They are science deniers that are living in the year 500s... Even then when Spherical Earth was a common thought and perception of the people, science discoveries using equipment was relatively a new thing. "Can't teach an old dog new tricks", and these Flat-Eather's are old dogs without brains to do their own research.