That too.
In the film, he hemms and hawws, and can't make up his mind of whether or not he wants to be king, but he never actually articulates a single reason for why he would not want to be one.
The film:
* Expects the audience fill in the blank for why he doesn't want to be a leader.
* Tries to make him more sympathetic as a leader, by turning him into a reluctant leader, as opposed to a guy seizing power because... Something something nobility, something something hereditary monarchy is how things are done in Middle Earth, but doesn't fly super-well for modern audiences..?
As I said in the essay I posted on my blog some time ago (link upthread), I think Jackson simply didn't understand Tolkien's conceptual scheme, and couldn't parse the idea that Aragorn is simply a man who is able to make the right choices because they are right, and to help others to make right choices too. Jackson is certainly not alone in this in the modern world.
Not only that, but even the character arc in the backstory (the Tale of Aragorn and Arwen) is nothing like the arc portrayed in the movies. Even as a young man, Aragorn is noble, confident, and driven: he is only twenty years old when he returns from great deeds in the company of the sons of Elrond and is told his true name and lineage, and from that point he knows he wants to fulfill that lineage; he is never in any doubt about it. His character arc is about all of the things he has to do and all of the knowledge he has to gain in order to be able to fulfill his lineage when the time comes.