Azula has not YET surpasses Ozai, and Iroh. Maybe not even Jeong Jeong, but she will. Zuko hasn't surpassed Jeong Jeong. He isn't that strong.

But personaly I think it's just because it's a children series, so the main characters are children. And the children who watch the sereis don't like weak main characters. So I think it's also a bit on purpose. But I think it's a bit weird.

BUT there could also be another answer, and that is that the kids in Avatar haven't surpasses/nearly surpassed the old masters, but maybe we think they did, because we saw them bend a lot more.

So you think they all happen to be progidy's? Could be, but that are lot's of progidy's with EXTREME LOT of talen. Esspecially Toph for that matter. But you think Jeong Jeong, Iroh, Bumi, Hama and Pakku have past their prime... That makes sense. They are all 60 or older, so 20 years back they would be stronger and more agile.

the protagonists have the "extra special" that allows them to assimilate things faster than others, and that would make them in the future "great masters"

it is easy to see it more clearly if we put in the equation someone all of you forgot just because he is the "non-bender", Sokka

these are the words of Piandao

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*before their battle

Piandao: Sokka, when you first arrived, you were so unsure. You even seemed down on yourself. But I saw something in you right away. I saw a heart as strong as a lion turtle, and twice as big. And as we trained, it wasn't your skills that impressed me. (Fat kneels to Piandao and gives him the sword) No, it certainly wasn't your skills. (Sokka looks down in shame) You showed something beyond that. (unsheathes the sword, showing its black blade) Creativity, versatility, intelligence…these are the traits that define a great swordsman. And these are the traits that define you. (sheathes the sword, kneels and gives it to Sokka) You told me you didn't know if you were worthy, but I believe that you are more worthy than any man I have ever trained.

than later on after the battle

Piandao: Oh, I've been around a while. You pick things up. (wipes the dirt off his face with the cloth) Of course, I knew from the beginning that Sokka was Water Tribe. You might want to think of a better Fire Nation cover name. Try "Lee." There's a million "Lees" (sips his drink).

Katara: But why would you agree to train someone from the Water Tribe

Piandao: The way of the sword doesn't belong to any one nation. Knowledge of the arts belongs to us all. (gives his sword to Fat. He pulls Sokka's sword out of the ground and gives it back to Sokka) Sokka, you must continue your training on your own. If you stay on this path, I know that one day you will become an even greater master than I am.

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basically is the same with the "benders"

Toph has become stronger thanks to her strenghts caused by her blindness(and in some cases, her blindness can be a weakness), but I don't think she could beat Bumi, and most people speculate that Bumi has learned to listen with his ears and that he might at least have the concept of metal-bending if not the use of it

Katara has become stronger, probably because her eagerness and intelligence; and she having to learn on her own until she met Aang. and even after learning bloodbending from someone else BTW, I don't think she would beat Pakku, perhaps now it will get to a draw, but defeat him? not yet, but she will surpass him someday

Azula had the natural talent and most of all hunger of power that made her someone that would try to put attention and learn from the things she saw, but she never surpassed her father

Zuko has perseverance and the spirit of never giving up even when he is down, at first his handicap was that he was not sure of exactly what he did want, many times his goals were from what others expected from him. But after the eclipse, and firebending masters, he saw that honor comes out of what you make of yourself, not of "getting approval" from others

unless Azula "finds goodness within herself", I can easily see Zuko becoming vastly superior to her sister

Mai, Ty Lee and Suki are highly skilled warriors, and until recently sokka could not be "their equal". all 4 I can't see beating Piandao, but I think all 4 would become great masters on their own right

Sokka being the stronger not because he is a "guy", but because he has the eagerness to learn from different styles and incorporating all of them into his way to battle

we saw that as the avatar Aang is stronger than any other mortal, but in "raw avatar" he has the skills he learned PLUS whatever other past avatars learned, as a raw avatar is all avatars in one body, but at the final part of his battle we can see that his eyes didn't stay lit up, they only lit up when he reached for his avatar state powers, and after that he used the movements Aang learned but in a stronger form.

so he will still have to learn new techniques and ways from Toph, Katara and Zuko and other masters; and he could learn one or 2 things from Sokka and incorporate them into his bending

That is what I call a plot hole. I basically tried to ignore this fact while I was watching the series

*raises flame shield*

But then again, I personally think that Bumi > Toph; Pakku > Katara; and Ozai, Iroh, and Jeong Jeong > Azula; so I'll call it a medium-sized hole.

*lowers shield ever-so-slightly*

Zuko and Toph would.

Zuko and Aang became almost equal in firebending after the FBM episode, but I think Zuko would win because he's more ruthless.

Toph would win because she's just plain better.