|Taken directly from Katara's relationships page.|
Iroh was originally one of Katara's enemies, albeit indirectly, as the firebender was aiding his nephew, Prince Zuko, in capturing Aang and restoring his honor in the Fire Nation, actually attacking the Avatar and his friends early in their journey. Katara and Iroh first met when Zuko and his soldiers formed an alliance with a group of pirates by means of capturing Team Avatar, who had stolen a waterbending scroll from the pirates, which resulted in Zuko taking Katara hostage. When Aang and Sokka were captured by the pirates and brought to her, Katara told Aang it was all her fault. He denied it, but Iroh agreed with Katara, which caused Katara to frown at him.
While the Avatar was learning waterbending in the North Pole, the Fire Navy attacked the Northern Water Tribe. Amidst the ensuing battle, Admiral Zhao was able to infiltrate the Spirit Oasis and attempted to slay the Moon Spirit. When Aang was unable to stop him, Iroh unofficially teamed up with the airbender and his friends by intervening and warning Zhao to let the spirit go, as upsetting the natural balance would not only affect the Water Tribe but also the entire world; when the admiral arrogantly refused and murdered the moon spirit, the old man defeated the rest of the Fire Nation soldiers before assisting Princess Yue in her sacrifice.
Some weeks later, a thoroughly sleep-deprived Aang was fighting a three-way duel between Zuko, Princess Azula, and himself; Iroh, along with Katara, Sokka, and Toph arrived to aid him. When Iroh was distracted upon finding out that Toph was affiliated with the Avatar, Azula seriously injured her uncle. Aang, Katara, Toph, and Zuko unleashed all their bending power at Azula who deflected it and with a firebending move, was able to escape. Despite a past of attacks against Aang, Katara bore no real grudge against Iroh, as the latter had merely accompanied Zuko on the exiled prince's attempts to capture the Avatar, nor did Iroh take issue with the waterbender. Regardless, Katara offered to heal Iroh only to be violently rebuffed by Zuko.
Later, when Zuko and Iroh were in Ba Sing Se and had opened the Jasmine Dragon, Katara visited the teashop with Momo, where she discovered her two enemies. Katara did not trust Zuko and Iroh who had come in peace to live as refugees at Ba Sing Se. Katara immediately rushed to the Earth Kingdom Royal Palace to divulge Zuko and Iroh's identities and presence to the Earth King. Not long after, Azula, who was disguised in the city as a Kyoshi Warrior, captured both Katara and Zuko. Iroh knew that Team Avatar was in Ba Sing Se and sought Aang, Sokka, and Toph to help him save his nephew from captivity, forming a permanent official alliance with Team Avatar and vowing himself not to allow Zuko to hurt or hinder Team Avatar ever again. Aang and Iroh made their way to the Crystal Catacombs and rescued Katara and Zuko from their underground prison.
At the end of the conflict at hand, Azula drew Zuko away from his and Iroh's good side and toward his and her evil side. Together, Zuko and Azula, with the help of the Dai Li, took down Aang and Katara until Aang lay dead in the cornered Katara's arms. Katara was helpless and thought all was lost as she carried her deceased lover's body in her arms. Fully changed from his days as the ruthless Fire Nation general and free from the clutches of Zuko to choose his own destiny, Iroh stepped in on the scene, there for no reason other than to help Katara escape, much to Katara's surprise. He drew the attention of their enemies, so that a reassured Katara carried herself and Aang out of the Crystal Catacombs to safety. When Iroh saved her and Aang's lives, he seemed to have befriended Katara at this point.
Katara and Iroh met again when the former and her companions, which now included a much changed Zuko sought the latter to help them defeat Ozai, as Aang had mysteriously gone missing. Iroh later helped the team to determine how they should assist in Ozai's final defeat when Sozin's Comet arrived. It is clear that he respected all of their abilities, as he did not argue when Katara chose her task to assist Zuko in defeating Azula, only offering encouragement. The two remained friends after the Hundred Year War.