This scene for many was the moment their ship was born or validated; but for a moment let’s just look at what this scene meant to the characters.
Zuko, who so viciously guarded his scar in the past, is letting an enemy touch him. I know, I know. She needs to touch his scar to get a feel for the damage done; I know he understands that. Most profound to me though is the fact that his eyes are closed. This shows a great deal of trust. He is trusting Katara; and Katara, in turn, is trusting him. These two characters are so…amazing. Both Katara and Zuko have done damage to one another; yet, in this moment, they are allowing themselves to be vulnerable in front of one another.
Even when they are rescued, I’ve noticed that Katara steps toward him while Zuko kind of leans toward her. If they were doing something they felt they shouldn’t be, they would have leapt away from one another. Point is: this doesn’t feel wrong in any manner. They aren’t ashamed to be found so close to one another. ((Not that they really have a reason to be ashamed or to feel guilty.)) Katara isn’t ashamed to be caught helping Zuko.
After they are rescued, Katara watches Zuko as she walks away. She keeps her eyes on him until she physically can’t look at him anymore. I don’t know if she expected him to follow Aang and her or not, but she looks sad/disappointed as she turns away.
Zuko, however, adverts his eyes. He is still confused and seems to be slightly ashamed as he looks away. I feel like he was torn. On one hand, he knew which decision was the right one; but, on the other hand, his chase of the Avatar–his misguided journey to regain his honor–was so ingrained in him that it confused him. He was struggling between the right decision and the easy path. Maybe that’s why Katara looked so sad/disappointed. She saw that he was still confused, but hoped that he would make the right decision in the end.
((Sorry if this made less sense near the end. It’s 2 am where I am and I’m tired. So, I’m going to end this here.))