Prince Zuko's dogged pursuit of Aang in Avatar: The Last Airbender to restore his honor in the Fire Nation served as the core conflict to the show's first season. Banished by his father and sent on a fool's errand to find the Avatar missing for nearly a century, Zuko served as the show's primary antagonist as time and again, he hunted the Airbender and his friends down only to face repeated failures that never deterred him.
What really makes the failure sting is that Zuko's quest never came closer than when he started. Looking at all his clashes with Aang during the series, Zuko's best chance at fulfilling his mission came and went in only the second episode of the series.
After 100 years frozen in an iceberg that removed him from the world during a century-long war he alone could stop, Aang's reemergence in the South Pole quickly alerts Prince Zuko to his presence. In the first two episodes of the series, Zuko tracks Aang down to the Southern Water Tribe, challenge him to a duel and almost immediately apprehend the Avatar he spent years searching for. Aang willingly gives himself up to Zuko's custody out of a desire to protect the surrounding members of the Southern Water Tribe, but even after he escapes, Zuko manages to recapture him almost immediately.
In retrospect, keeping in mind just how much Zuko struggled subsequently throughout the rest of the season, it's remarkable to rewatch "The Avatar Returns" and see just how easily Zuko apprehends his quarry. In their first bout, Zuko holds his own, and it's his threat to the surrounding civilians that causes Aang to forfeit. In their next bout on Zuko's ship, Aang quickly evades Zuko and briefly incapacitates him, but Zuko's response is to immediately recover and chase Aang down, quickly overpowering him. In the end, it's only the sudden emergence of the Avatar State and the hasty rescue of Appa that allows Aang to escape Zuko's grasp. The Fire Prince would never come so close again.
That was not for lack of trying, of course. In "The Warriors of Kyoshi," "The Waterbending Scroll" and "Bato of the Water Tribe," Aang repeatedly proves to be the superior fighter or cleverer thinker when it comes to resisting Zuko's attempts at capture. In the lattermost episode, the two even engage in an extended duel, where Aang's training in waterbending allows him to gain an edge he didn't have in any of the pair's earlier bouts. Throughout the rest of the series, Aang only ever gets stronger, and it seems Zuko squandered his best opportunity.
Perhaps the most notable instance of Zuko nearly capturing the Avatar came in the finale of the first season, where Zuko manages to whisk Aang away from the Nothern Water Tribe only to find a blizzard and no support in the climes outside. There's simply nowhere to go, and it's only a matter of time before Aang awakens and his friends catch up to rescue him. However, in his first encounter with the Gaang, Zuko proves his superiority, had all his men on hand and even had the Avatar restrained in his ship. It all fell apart because he didn't know exactly who he was dealing with.
Leaving unremarkable guards alone to escort Aang to his cell proved to be Zuko's first mistake, but failing to understand or appreciate the full power of the Avatar State proved to be his undoing even thereafter. With just a little more experience, Zuko very well could have won his honor all the way at the start of the series.
Of course, things would have turned out quite differently if that had happened. Zuko underwent one of the greatest redemption arcs in fiction, but there would have been no shot at redemption if his attempts at antagonism were not so frequently foiled early on. Things worked out in the end, but it took some major stumbles to get there.
