It is not a great tool for understanding what is "wrong" with people, or for communicating with people who are wrong. Flat earthers are not wrong because of science, they are wrong because of society. That is, most flat earthers turn away from our shared perception of the world because of some trauma in their lives. They have lost trust in something that they felt was solid.
You may think that you believe in science because you are a logical person, but you really believe in science because people you respect believe in science. Science also has the benefit of actually working, which is nice, but many things can LOOK like they are working (epicycles of the planets, flat earth, miasma theory of disease). You can make scienticious (sic) sounding observations about all of these things.
The point is that when you want to understand why people are wrong, you need to think about motivation and deeply held beliefs, not proof. Scientific proof is obviously very useful, but before you use that, you have to get them to come closer to you.
Imagine a person standing on a hill. If they are shoved and fall down, they roll down the hill. Using the strongest arguments feels like the most effective thing to do. Strong arguments do move people, but you don't get to choose the direction they move.