Ok before I start I just want to state that I'm a Zutarian but by no means do I diminish Kataang's importance. With this said I'm going to start my crazy analysis.
Before this begins I did some homework and researched body language. So this is some of the things I came up with on the net.


Emotional body language (like the hug Katara and Zuko share) - Identifying feelings.
Up close

When you are close to the other person, the body language progressively gets more intimate until one person signals 'enough' if that is what she wants.

Close in and personal

In moving closer to the other person, you move from social space into their personal body space, showing how you would like to get even closer to them, perhaps holding them and more...

Standing square-on to them also blocks anyone else from joining the conversation and signals to others to stay away.

Lovers' gaze

When you are standing close to them, you will holding each other's gaze for longer and longer periods before looking away.

Touching

Touching signals even closer intimacy.


I know we all have seen this between Zuko and Katara even though they may not mean a romantic relationship they show intimacy. So what goes around my mind is how in the world would they be intimate with each other at some points when they were supposedly enemies? There you have it, most of the signs above are about CoD. Katara went from far from Zuko in terms of space, which represents social space to a few inches away from him. When someone gets that close it means the person that is stepping closer wants to get in the other's personal space, showing intimacy with the other. Like many have said there was a connection between Zuko and Katara at that particular moment and with that connection came emotional intimacy. Of course she is also intimate of Aang, but the difference is that Aang is Katara's best friend. It's common to have that kind of intimacy between friends but with a person you hardly know and that is, in theory, your enemy is quite intriguing to me. The only explanation is that there was enough material in that talk of theirs to create intimacy and connect them. With this said I just want to point out that with such bond created between two people it is extremely difficult to break it, what made me sure, from that point on, that even if Katara got extremely angry at Zuko for betraying her, she would eventually forgive him.

So I will not talk about the body language in both of the Kataang kisses but if you are interested to know look that out on the net or something. I just want to say that both theories of embarrassment and/or surprise are both corroborated by body language rules.

So going on to the Zutara hug.
There are so many types of hugs that it is hard to know where to start in explaining their differences. So many variables affect the types of a hug that people give each other. For instance, people’s height, weight, age and their relationship, all determine the kinds of hugs that they give each other. Not to mention whether the huggers are men, women, friends or lovers!

First, there is the friendly hug. This type of hug usually happens between friends of either the opposite or the same sex. Family members also give each other these types of hugs. It is a caring, yet short embrace and may or may not involve a kiss on the cheek, depending on the situation and who the people are to each other. Generally, family member hugs include a kiss on the cheek but not always. If a younger person is hugging a senior relative or friend, the younger person often kisses the older person on the cheek. The kiss on the cheek is both a sign of respect and friendly caring or affection. The older people may also kiss the younger person on the cheek, or forehead. These types of hugs are usually done while standing or sitting down.
This makes me think of most of the Kataang hugs and kisses.
But notice that Zutara hug. It shows despair. I was neutral when I analyzed this, so in my personal opinion it's not a romantic hug but still... It shows how desperate Katara is to find someone with identical feelings. Just look at her face. There is a mist of feelings. Some may be missing but what I see there is shame, sadness, forgiveness and happiness.
Yes that single expression told me all of that. Of course it's corroborated by the expressions on her face while she listens to Zuko and when she lunges towards him. We can see that she is no longer ad at him and that she feels like he shares her feelings.
Now pay close attention to his body language. At first when he is talking to her he seems sad, ashamed. That makes me strongly believe that this talk will be not only about Katara's mother but also in some way (even if it's not directly) about what happened in Ba Sing Se. I don't know if I'm the only one seeing this, but it seems to me that both Zuko and Katara are smiling (not showing teeth of course, it's a discrete smile) to each other. His expression take us to an understanding atmosphere while hers takes us to not only an understanding atmosphere but look at her eybrows on that one! She looks as if she sees him as an intimate friend. That expression says it all. ZUko is dear to her ( not in a romantic way, I keep on pointing out). Katara is really straight but ZUko is slightly hunched forwards, which by the rules of body language means he wants to go closer to her. It can be both physically or emotionally, like we stated before they bonded. They both seem very peaceful and unaware of their surroundings. Then when she first move towards him her expression seems to light up. She seems happier with what is happening and she is the one to make the move. Note her body posture. Her arms are slightly forward and she is taking a step. This means that it is a willing situation and it is her intention to do so. Now look at Zuko. His hands come slightly forward which means he is defensive and taken by surprise. His mouth is slightly open which also means surprise but his eyes are not wide which in my opinion represents a sudden ease with the situation. It is surprising but at the same time it's not that surprising he is going to back off of it. The when Katara's arms are already extended to Zuko's neck we can see that he is now worried. His arms and hands are more forward than before which means that he wasn't expecting her to go all the way. His eybrow is curved upwards and his eye is a little wider which also represents a kind of unexpected surprise. Note me when I say unexpected. It could be a surprise that in the back of his mind he had imagined or wanted but his expression tells me that he never even considered it before. Now look at Katara's face: Still one of contentment, which means that she is happy she is so close.
Now one thing that I noted are her fingers, it looks like she is ready to hold onto his shirt, once more signaling towards intimacy.
When she is already very near him and we can't see his face, we can't still notice his surprise by his hand position. Ok now when i saw this pic I laughed a bit. Is it just me or Katara has a somewhat pervy look plastered on her face?
Ok now I can't really make out if it's a smile wide smile upon her face or just her lips curved upwards in a normal smile so i really can't tell you, but by this point you already note the dispair in her. The fact that it wasn't just one of those hugs where you walk to the person and embrace her says toons. She ran towards him. Once again dispair and emotion taking a play onto this. It means that is something she craves, she needs and is spurr of the moment. Something triggered her into that hug, and although it's not a romantic hug it's a fierce and passionate hug.
Moving on. On the next pic her expression changes, she seems sad. When I look at this I see her pouring her heart to him. If that doesn't happen, at least that is what she wants. That expression on her face means that she found someone who can understand her. Now look at her body. Even though she is close to him, their bodies aren't pressed. She wants that intimacy but it isn't a total intimacy, it only goes that deep. Zuko is still surprised on this one, but what really surprised ME was his reaction to this.
He wrapped his arm around her lower back, pushing her towards him. AND NOW THIS MEANS TOONS PEOPLE. I was watching the Boiling Rock and when Suki and Sokka hugged you saw a perfectly normal hug. Now notice where Sokka's hands are. They are on her upper back, showing that same intimacy but in a lower level. He respects boundaries and even though she is his girlfriend that hug suggests that there is note enough tightness between the both of them for him to take that step a put his hand on her lower back. Now back to Zuko. His hand being on her lower back is really important. That means that there is not only intimacy between them but it's a higher kind of intimacy, the kind that doesn't notice the physical.
You go ahead and ask me "Why is it that important?" and now I ask you WOULD YOU HUG SOMEONE YOU HAD NO CONNECTION, NO INTIMACY, NO CLOSENESS TO AT ALL LIKE THAT? WOULD YOU TAKE THAT STEP AND PUT YOUR HAND JUST INCHES ABOVE THAT PERSON'S BOTTOM? WOULD YOU LET SOMEONE YOU HAVE NO FEELINGS WHATSOEVER ABOUT, OR EVEN IF IT'S A FRIEND GO THAT FAR AND PUT HIS OR HER HAND THAT LOW?
I know i wouldn't
Now to finish off with Zuko, notice his expression (even though we only see his eye) we see the same despair that is in Katara, we see understanding, respect, sadness for the other. This shows us that he cares about her. HE DOES! Just look at all the times he didn't fight her back when she said stupid stuff. He didn't want to get involved into arguments. When she threatened him did you see his expression. He felt disappointed. I bet he thought she would be the first one to welcome him but when she didn't see him that lightly anymore it hurt him. And now when he is hugging her you can see the same. You can see the care he has for her. Now i'm noting his shoulder, they are slightly hunched forwards which i think it indicates that his chin is rested upon her shoulder as well indicating that intimacy and care he has with her and for her.
Now look at Katara, her face means a lot. it symbolizes her sadness over something but also that bond between her and Zuko reforming. It's understanding.
Look at her arms. They are around his shoulder not his neck. So this firmly tells me that this isn't at all romantic. But.... they are tightly around his shoulders.
Shoulders have a very important symbolic status. Remember Atlas, that man that was forced to carry the weight of the world on his shoulders? Shoulders are a very rigid, strong part of one's body. They are capable of sustaining great weights and are considered to be the part in our bodies with a similar importance to the neck.
Shoulders symbolizes strength, protection.
So where am I going with all this?
By holding onto Zuko's shoulders Katara is expressing weakness. She needs protection, she need someone to lift her weight from off of her. And this is very important because that person is Zuko. You can see it's a very tight grip which adds further to the representation of her weakness, her sorrow. And he is her pillar, her support.

Like I said before this may not indicate a romantic relationship but it does indicate that their relationship is:
- Strong;
- Intimate;
-Emotional;
- And they are each others pillars, each others mirrors.

I mean I think this explains a lot why Zuko and Katara are yin and yang. Although they are different and need each other to balance themselves (look at that hug, they are both using each other for sustain) they are also the mirrors of one and other.
Just look at it, their body language differs throughout the aproximation, but when they both reach that climax, the hug itself, their body language is the same. She need support and he gives her (her hands on his shoulders, his hand on her lower back) He needs support and she gives him (his chin on her shoulder.)

SO after my rant I say goodbye. Whether you agree with me or not you do have to admit that it's going to be a very good moment in the series.