Narrowness of mind is often the cause of obstinacy; we do not easily believe beyond what we see.

Stubbornness usually looks like strength of will and is more often a shortage of imagination. If you cannot picture the alternative working, refusing it feels like good sense rather than fear, and no amount of argument helps because the problem is not the argument. The person simply has no image of the other way vivid enough to weigh against the one they know.

When you are immovable about something, stop defending the position and go and look at the alternative in the flesh. Talk to someone who lives it, visit the place, try it for a week, and let your imagination be fed by something other than your own supposing.