I think there is a very good argument (well, there is hundreds, but this one, Flat Earther's will have an even more difficult time to explain) against Flat Earth.
Look at Australia and Brazil and South Africa, on their stupid flat map.
Now, put an Australian, a Brazilian and a South African, all using a compass and looking south, which on flat Earth is the opposite of the "center" of the map.
While looking north, all of them are looking towards the center of map and could see the same "star" (north star), when looking South, they look at different directions.
An Australian and a Brazilian look at exactly opposite directions.
How can an Australian, a Brazilian and a South African, while looking at such different directions, ALL SEE THE SOUTHERN CROSS when looking south?
I've been thinking about this, trying to come up with why this isn't a good argument.
Of course, logically, it's a perfectly good argument. Of course it is correct. Unfortunately, it would persuade no one, because the people it is aimed at do not think scientifically. They aren't interested in testing their theories to see if they are correct. They have read the Bible. They know it is right. From there, they want to seek confirmation of their correct theory. If someone presents a logical argument, and they cannot refute it, they will attribute their inability to refute it to their own lack of knowledge of "unimportant" things, or maybe to the conspiracy that keeps "the truth" away from them.
What I mean is, the reaction from a flat earther to that argument is likely to be something along the lines of, "Well, I'm not sure about that. I'm not some great math guy who can figure it all out. I just know that flat Earth scientists have figured it out exactly, but the scientific establishment won't publish their papers."
So, I've been trying to figure out what would be a good argument that might actually convince them. First, I conclude that the argument has to somehow be about people, not data. You can't argue stars and measurements and geometry with these people. The most powerful argument would be testimonial from someone they respect, like an athlete, entertainer, or preacher, but only ones that have somehow escaped the influence of the Whore of Babylon, and those are hard to come by.
Here's the best I could come up with, and, frankly, it is not very good.
Note to the flat earther that you can look up on a website, and determine the time of the next eclipse visible in your area. They can publish those dates years in advance. They are confident. They know it, and they are always right. They never make a mistake about this stuff. Furthermore, when they do that sort of thing, they say that they have to use a round Earth model in their calculations, and it works. How could that be, if the Earth were flat?
What this does is translate this out of the world of geometry into the world of people. You aren't asking the flat-earther to describe the geometry of eclipses. You are asking him how scientists are able to predict eclipses. They say that they are using a round Earth to do it. Also, the phenomenon in question, the eclipse, is something the flat Earther can see himself. A television program can be faked, but the eclipse happens right before his own eyes. The scientists say that they knew it would happen because the Earth is round. Are they lying?
It's hard to imagine any argument working against an adult who believes the Earth is flat, but something along those lines, which turns it into an argument about people instead of geometry has some hope. Moreover, the same issue is encountered dealing with issues more important than the flat Earth believers. The arguments about a young Earth versus old Earth have to be approached the same way.
