Why would you believe them, is a better question...And just why should such a challenge exclude the use of NASA or the military? Because flat earthers likely tend to be conspiracy theorists. People have flown around the world and others have sailed. When one is high enough in an airplane one can see the curvature.
There is zero reason to dismiss NASA and the military as it would require a conspiracy of massive proportions that would be utterly impossible to keep quiet. As for those who use the Bible, they will use God sitting above the "circle of the earth" and conclude that the earth is a flat circle, all the while ignoring Rev.7:1 where there are "angels standing at the four corners of the earth," or vice versa. Circles didn't have corners the last time I took math, but perhaps that was NASA based math.
The whole idea of a flat earth is just silly.
Let's look at the images of earth, that we have from our only source....NASA..
Apollo 17, 1975. The most popular image and used in every textbook.
Now, lets look at some more:
Check out the scale of the continents. They are all over the map, pardon the pun...some are huge others smaller.
In one image they have found that cloud formations are photo shopped and pasted all over the CGI image. One cloud formation found in many places on the globe in the same picture.
Also, NASA admits that they are not real photos but "composites" photos.
The Apollo 17 picture of the earth, from the moon, is photo shopped into the image.
Videos of the earth, from space, over a 24 hour period, show absolutely no cloud movement.
There is a short movie of the crew on one of the Apollo missions as they photograph the earth out their round window to make it look like a ball earth.
OK, let's ask the big question. NASA spent billions upon billions of dollars on this program. Out of all the times they went to the moon, they have ONE picture. If I went to the moon I would take many pictures.
So, no, I do not trust NASA. Not when they photo shop the earth into a moon shot picture and photo shop clouds onto a supposed picture of the globe and they cannot even show us multiple pictures of the globe earth, from space where the continents are at least the same size.
I don't know what they are doing, but it is not trust worthy.
If you want to see the photoshop of the earth in the picture taken from the moon, you can do it yourself, if you have photoshop. Rob Skiba, shows how he did it in this youtube clip...he also explains what I have been talking about here too.