I was perhaps 9 or 10 years old when I told my father that I was due for a raise in my weekly allowance, from 15 cents to 25 cents. (Yes, this either dates me, or says something about our socioeconomic status, or both.)
I explained to him that 25 cents was the going rate.
"How do you know that?" he asked.
"All my friends are getting 25 cents," I replied.
"Who, for example?"
"Suzy next door."
"How do you know that Suzy next door is getting 25 cents?" he asked.
"She told me."
"So all you know is that Suzy told you she's getting 25 cents. You don't know that she's getting 25 cents. For all you know, she's telling her parents that she wants a raise since you're getting 25 cents."
"Are you saying my friends are lying?" A weak and angry retort, but it was the best I could do. I had already lost. I think we compromised at 20 cents.
It's true that my training as a mathematician, especially at math summer camp when I was in high school, helps me distinguish true from false, and true from "someone told me it was true". So I'm continually surprised when I see mathematicians fall for false "proofs" or fake news. But then I remember that I had the additional benefit of learning from a father who was a newspaper reporter back in the day when journalism was supposed to be about facts, not opinion.