It's a lovely thing when you can write, an entertaining, compelling story where your main character goes through some transformation or learns a valuable lesson during their journey to overcome a challenge or solve a problem. A great example of character arc is Michael Corleone in The Godfather, who is a college graduate and war hero that returns home and becomes involved in saving his father's business, which is a crime family.
Towards the end of Godfather Part Two Michael earnestly asks his mother about losing his family:
MICHAEL
Tell me something, Ma. What did Papa think -- deep in his heart? He was being strong -- strong for his family. But by being strong for his family -- could he -- lose it?
MAMA
You're thinking about your wife -- about the baby you lost. But you and your wife can always have another baby.
MICHAEL
No, I meant -- lose his family.
MAMA
but you can never lose your family.
MICHAEL
Times are changing.
Michael's arc is that he's willing to resort to crime and murder to protect his family and ends ups losing his wife, and murdering his own brother. That's pretty far from the clean marine in Godfather Part One who assures his girlfriend Kay he's not involved with his family's nefarious activities.
I never spend much time deliberating what my protagonist's character arc is going to be. I think in terms of goals and objectives, whether moral or immoral, legal or illegal and that usually provides me with an arc by the end of the story. Nevertheless, I think it's very important that you can articulate your main character arc when pitching your work.
If you're interested in further reading, here's an article about a character's inner arc from Screencraft's website. https://screencraft.org/2020/07/27/acceptance-revelation-contentment-exp...
I think of it more as a character’s realisation. Their acceptance of the world and falling in lie with it. People only change under pressure.
Try writing a short character driven script - it's harder than you think.
One theory I studied many, many years ago defined the hero's arc as:
Man v World - where Man changes to view the world differently ("World" can mean the actual world, or his own self-perception, or anything in between - and "differently" can mean more clearly/truthfully or more muddled/delusional, or anything in between)
And anti-hero arc is where the hero REFUSES to change, despite the World's best efforts.
Both of these are active, conscious decisions (to change or not) - any plot that doesn't give the hero that choice doesn't have an (character) arc.
While I firmly believe this philosophy (and write that way), it certainly isn't the only way to view arc.