How do you distinguish between can't and won't?

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At what point does something go from being something you won't do to something you can't do? For example, if something puts you through immense suffering, might cause meltdowns, and is something you deeply dread, but you could possibly force yourself through it, is that something you can't do or won't do?

That meets my definition for "won't do". Or even "shouldn't do", but not "can't do".

...but, I probably use a very literal meaning for "can" and "can't". It's gotten me in trouble in the past.



Something you "can't do", to me, is something that is impossible, not improbable, and not very difficult...but impossible. Very few things will meet that criteria.

The "pool" test.

Throw 'em in. If they drown, they really can't.

Drowning equating from an outsider's perspective to, you're only hurting yourself with what you're doing. "Can't" hurts itself because it can't actually do it, no matter how much it wants to. "Won't" will do it for sake of self-preservation.

it's "can't do without negative consequences."

Can't means the person does not have the knowledge or skills to perform the task.

Won't means the person has the skills and knowledge, but willfully refuses to do the task.

on another forum the subject was as a kid do you eat whatever's put before you.
and i talked out how my sharp senses to taste, smell and texture make me a picky eater.
but it's hard for me to know for sure what foods i can't eat and what foods i won't eat.

What's the context for this? In other words, what is the significance of the distinction, other than the definitions of words?