Why your protagonist's longing should lead to their fear
What your protagonist longs for is what they'd have if their deepest fear didn't run them, so chasing it should walk them into that fear, or the longing is decoration.
What your protagonist needs moves from something they'd deny, to flickers they push back down, to something undeniable once their false belief breaks, and that movement is the arc.
Your protagonist's arc is their real need moving from something they'd deny to something they can't deny anymore.
Your protagonist has a desire they can name, what StoryDNA calls The Want. What would actually make them whole is The Need, and it surfaces in three stages.
Early on, The Need is out of sight. Your protagonist doesn't know they need it and would push back if you told them. If they state it in the opening act, it isn't a need yet. It's a plan.
In the middle, The Need flickers up. A moment of exhaustion. A conversation that goes further than they meant. Then they shove it back down, because looking at it would mean questioning their goal.
At the crisis, The Lie, the false belief they've lived by, finally fails, and The Need becomes impossible to ignore.
What people need tends to surface in their weakest moments, and they push it back down before they can look at it.
In Cast Away, Chuck's conversations with a volleyball named Wilson show how much he needs people, a need he'd spent years putting behind his schedules.
Plant the flickers mid-story, in scenes where your protagonist's guard is down, and let each one retreat. If The Need shows up at the crisis with no earlier flicker, your reader will feel it was dropped in, not discovered.
What your protagonist longs for is what they'd have if their deepest fear didn't run them, so chasing it should walk them into that fear, or the longing is decoration.
Nearly every goal carries a selfish version, how your protagonist would get it if nobody else counted, and that version is what the turn asks them to give up.
If your protagonist wins the goal without changing and the story treats it as a triumph, the story has adopted their false belief.