His face had been the face of the enemy from the moment Katara had laid her eyes on him. Scary, tainted, scowling, his face was simply everything the face of the enemy should be. Even though her logic told her that he couldn't possibly have been the man who killed of mother, it was his face that came to mind every time she pictured that man. It was his face that haunted her in her nightmares. It was his face that she hated
But that started to change when she saw him without his ponytail. His face showed that he had cut loose some sort of emotional bond, one that forced him to do the things that he did. And when the general got hurt badly, his eyes (the enemies eyes) betrayed his hurt and the fear of losing the only person he had left in this world. That's why Katara offered to heal him, the general, just another enemy out to capture Aang, but most importantly, the only one caring for the lost boy that suddenly replaced the scar( r)ed prince.
So when she saw him in the catacombs, locked away by his own sister, she took pity on him. His situation was much worse then hers was, but still she couldn't help but fend off her anger at him, having pictured his face as that of the enemy for so long. But after realising how similar they were, when he shared that he too had lost his mom to the fire nation, she wanted to rid him of his scar, healing him from whatever he had suffered, but it also was a selfish act, for it was necessary for getting over her hurt herself, for she no longer saw him as an enemy.
And then he betrayed them, betrayed her personally, and it all came rushing back. It seemed like it was her destiny was to hate him, and at that time, she would have embraced that destiny. So when he appeared in their camp, claiming to have changed for real this time, she didn't believe him, wouldn't believe him. She vowed not to let herself get hurt by him again. She threatened him, pestered him, angered him, humiliated him, all to get the others to see his true nature. But he never faltered. He let himself undergo all she put him through that with a smile, for he was truly sorry.
When she found out who had killed her mother, Aang judged her for wanting to go after him, Sokka gave her a lecture for wanting to leave in such a dangerous time, but he volunteered to go with her. Deciding that she was just as bad as he was, she was going to take another persons life after all, she agreed to let him come with her. Atleast, that's what she kept telling herself. Deep down, she was touched that he was going to support her when everyone else shunned her, and this situation reminded her of the catacombs, only this time he didn't betray her.
When they got there and she was practically killing that man, he didn't stop her. He just stood there, amazed at what she could do. So naturally, on the way back, she asked him why she didn't stop her. His reply was quite simple : "Who am I to judge you? You're a much better person then I ever was and ever will be, and if you thought it was necessary to kill him, you would have done so regardless of what I would have done. I trust your judgement. And to be honest, I think he deserved it. He took your mother away, he made you go through a lot of pain, and you're still suffering because of him everyday"
That meant the world to her. For once she didn't need to be strong, she wasn't the mother of the group, she was allowed to feel sad. So she did the only logical thing she could think of. She semi dived into his arms and sobbed her heart out. And much to her surprise, he hugged her back, pulled her close and told her that it was ok. That she did the right thing, and that she was allowed to show her emotions.
By the time they got back to camp, she had her emotions back in check, so when they got off of Appa, she gave him one last hug and told him that he was forgiven (as if the moment on Appa hadn't told him so) and unknown to her, that meant the world to him.
Katara was finally able to let go of her grudges towards the fire nation. But most importantly, she no longer considered Zuko as the prince, or the enemy. Now when she thinks of his face she sees the face of a friend, of someone who has gone through his share of pain, and was willing to take some of her burdens onto himself.
She could finally move on from the darkness into the light. And unknown to her, she had enabled Zuko to move on as well. He finally redeemed himself for all that he had done in the past.
And together they moved on to their final battle, the battle against Azula. The first thing that Katara noticed was that something was off, but she couldn't quite put her finger on what it was. Zuko realised it too, for he accepted Azula's challenge, an agni kai, even though she was supposedly unbeatable. Zuko dominated the agni kai at first, but then the odds changed when Azula broke all rules and directed her lightning towards Katara. Too shocked to move away, she could only watch her inevitable doom approach and then a something blocked her view and a scream pierced the quietness. When she opened her eyes, Katara saw Zuko lying on the ground , in front of her, chest marked by lightning, and something snapped inside of her. She tried to reach Zuko as fast as she could, but she had to beat Azula first, losing precious minutes that she could have used to heal Zuko. So when she finally reached him, she prayed to every god she could think of and it worked, she was able to heal him.
From that moment on, Katara knew she couldn't leave Zuko, Katara knew she wouldn't want to leave Zuko. Even though both of them felt obligated to love the persons who sacrificed so much for them back, they couldn't stop being drawn to each other. Both of them were waiting for a time in which they could move on to a different future, a future in which they could be together.