"Thinking in Bets" by Annie Duke describes this. One of the problems we have, societally, is talking in black and white. I'm right or wrong. It is extremely hard for anyone to admit they are wrong. In fact, a good way to push someone more strongly into their belief (regardless of what it is), is to tell them they're wrong.
Her approach was to start using confidence numbers or percentages, and being less black and white.
> "I'm 80% sure the it will be a sunny day tomorrow"
> "You know, I'm not sure about that. Have you considered the vast storm clouds and weather reports about the incoming rain?"
Both of these, by each person, make it easier to take, psychologically. You neither commit to something nor do you tell someone else they are wrong.
There are also synonyms for "wrong" which can soften the blow. For example "inaccurate", as in something like "unfortunately your response to the question is inaccurate because since version 5 that is no longer true."
By doing this I'm making it clear what is wrong, and not using the word "wrong". This separates the person from the statement, and by implication does not make their statement theirs.
Contrast with "you are wrong", which makes the statement personal, and implies the _person_ themself is defective.
A flat-earther has an inaccurate source of information, and has come to a misinformed conclusion, resulting in a unfortunate assessment of the current earth shape. If we start there, and recognize that (to a much lessor degree) we all have blind-spots it helps to engage with them.
But the quote above is true, you cannot rationalise people out of a position they did not rationally get in to.
Her approach was to start using confidence numbers or percentages, and being less black and white.
> "I'm 80% sure the it will be a sunny day tomorrow"
> "You know, I'm not sure about that. Have you considered the vast storm clouds and weather reports about the incoming rain?"
Both of these, by each person, make it easier to take, psychologically. You neither commit to something nor do you tell someone else they are wrong.