How do you teach non-technical coworkers to trust you're doing your work to the best of your ability? You know the type, they're used to having everything measured by simple numbers. Number big = good work. Number small = bad work or slacking off. The moment they run into something that doesn't work like this, their heads explode.

You threaten to quit.

And then you quit.

You can't "teach" those kinds of people anything.

If a person isn't willing to learn you can't teach them. If they're willing to debate you may punch through with convincing examples, but debates require intelligence and these people usually rely on oversimplification because they're dumb so they probably aren't actually imagining a debate. If they aren't even willing to seriously discuss the idea, you can contribute to their timely extraction from the market by quitting.

Start with the nucleat plant output chart:
small - mildly bad
medium - good
high - very bad

From there take it to other more nuanced examples

In the end, lots of things cand be represented as numbers, you just have to adjust the perspective and know what to count, what to sum and what to multiply

we have the same issue at work. it's good to build a reputation, show some good faith. don't say an outright "no", go with a "maybe" and later say it wasn't possible, so they "feel" you at least tried.

another thing that helps is being backed up by a colleague. one could be slacking off, but if two are telling them something, it's harder to take it as bs