Aragorn's Arc is A Positive Change Arc from Self Doubt to Self Acceptance not just as who he wants to be as his own individual leader but the leader of the grand legacy prophesied by the Ancient Kings who were once his forefathers. Aragorn is reluctant at first to be the leader the world needs him to be.

The fact that he has the cover name Strider that he goes by not only to protect himself from being seen by his enemies but it also tells us he suffers through an identity crisis.
Over the course of the story we learn that Aragorn is the heir to the throne of Gondor. We're constantly reminded of his lineage. He is challenged by Boromir at one point. Arwen encourages to accept the role laid before him that he's meant to do and see it through. And near the end of the movie of The Fellowship of the Ring we see him step into the place of the leader role once Gandalf is lost. Aragorn is the one decides to keep leading the fellowship after Gandalf is out of the picture. At the very end of the movie Aragorn declares that he will allow Frodo to head out on his own and instead that he and the rest of the group will focus on rescuing Merry & Pippin. This is Aragorn's turning point in the first movie we get to see a significantly difference version of him from whence we met him in the Prancing Pony. This is Aragorn taking those first steps of a rightful king. He is using power in order to protect the weak. Accepting who he is at last, Skylights.