I just watched Aragorn vs. Toxic Masculinity, which is a wonderful discussion of Aragorn as a quintessentially masculine character who is simultaneously tender and affirming. I've had the thought that Aragorn's greatest, defining moment in the movie comes at the end of The Fellowship of the Ring, when he meets Frodo in the woods, at the Breaking of the Fellowship.
If you recall, Boromir has just tried to take the ring by force. Aragorn has sought Frodo to ensure he is safe, but when Frodo sees him, he backs away. "Can you protect me from yourself?" he asks.
Aragorn is caught between two destinies: the Ranger and the King. The Ranger is all he has ever been, the man who works in the shadows, fights evil, defends the weak, and stays apart from the affairs of men and kings. Royalty is his heritage, but the last man to claim this heritage, Isildur, was destroyed by the temptations of power. If Aragorn could have his way, he would stay the Ranger. He fears the kingship, and the temptation it entails. He joined the Fellowship to do good as a Ranger, not a king.
In the book, it is clear that both destinies stay with him on the journey with the Fellowship. Once they draw near to Gondor, Aragorn knows he must choose: turn right, to Gondor, and become king; turn left, to Mordor, remain the Ranger. When Gandalf falls in Moria, Aragorn is left as the leader of the Fellowship. His destiny is now clear: he must choose the path he wanted to choose, be the Ranger, lead Frodo to Oroduin.
There on the banks of the Anduin, Frodo throws this destiny into doubt. If he goes with Frodo, he could be a risk to the quest. Frodo has determined that he must go alone. In the movie, Frodo makes one last effort to avoid his fate. He offers the ring to Aragorn. Will you go, instead of me, and destroy the ring? The offer is probably the cruelest thing Frodo could have done to Aragorn. "Here," he has said. "You can escape from the destiny you fear. All you have to do is take the thing that is the source of all you fear."
But it is mercy, as well. Frodo's offer makes plain to Aragorn: the path of the Ranger is not free of temptation, it is not clear, it is not easy. When Aragorn refuses--an act few people in Middle Earth are capable of, to refuse the ring of power--it is not just his fear of temptation. He sees that this one before him, this hobbit Frodo, might be the one who can do this deed. There is something else that Aragorn can do, instead. He can be the king of men.
He folds Frodo's hand over the ring, and pushes it away, and says only, "I would have gone with you all the way. Into the very flames of Mordor."
Moments later, an army of Orcs appears, and, while Frodo flies, he turns and salutes them with his sword. He is ready. He cannot bring the ring to Mordor. His destiny is to stand and do battle.
Aragorn never forgets this moment on the banks of the Anduin. After the Seige of Gondor, when he stands as the hero of the hour, when he has rode into battle under the flag of the kings of Gondor, still his thought is with the hobbit he had pledged to protect. So he conceives the maddest of all strategies: a suicide assault on the gates of Mordor, to create a distraction, and give cover for Frodo's mission.
The purpose of his mission is never forgotten. When they are surrounded by the hosts of Mordor, and he has made his rousing speech--"On this good earth, I bid you stand! Men of the West!"--he then turns, and says quietly, "For Frodo."
The final moment, of course, comes at his coronation. Sauron is defeated, Aragorn is crowned king, and he is finally reunited with his elven princess. As he is walking through his people, and all our bowing before their king, he meets Frodo and his companions, and says, "My friends. You bow to no man." He drops to his knees before them, and all Gondor sees their king kneel. Most have no idea why, but if their king is kneeling, they all fall to their knees. All Gondor kneels to four hobbits from the Shire. Because Aragorn knows that what he has done, becoming king, that was actually the easier path than the one he had intended. It was Frodo made Aragorn king. Then he went on to save all Middle Earth.