Uncle Iroh is the passive character yes? Totally unbiased, wise and morally good. He single-handedly led Zuko from crazed honourless Avatar hunter to world saviour over the course of three seasons....so....why did he never do the same to Azula?
Here you are already IMO making a wrong description of Iroh. You describe him as a passive, morally god, wise and unbiased person and then consequently try to show he is not like that, but frankly Iroh IMO never was like that in the first place nor was he shown like that nor do I doubt he would ever describe himself as such.
He is definitely a wise old man and he is not immoral. However I don't think he described himself a ever being 'morally good' nor will he ever considered himself as such. He fought for the Fire Nation for the longest part of his life. He besieged Ba Sing Se for years and what we know about his relationship with Azulon it seems the latter could be nothing else than being proud on Iroh. Iroh also helped Zuko with his quest for the Avatar and these are all things Iroh was very well aware of. He was a moral man, but your description of him being 'morally good' is something you tagged him with, not Iroh himself, so invalidating that is pointless.
What Iroh wanted the most was simply for Zuko to be happy. If Zuko would have been happy serving tea for the rest of his life in Ba Sing Se, I sincerely doubt Iroh would have done anything to change his mind. Iroh believed though that if Zuko would still try to involved himself in the Fire Nation's war, that trying to become what Ozai wants him to become would never make Zuko happy and that they only way to find peace in himself was to go against the current Fire Nation. A result of this is that he would never consider himself to be unbiased either, in fact it's the opposite. He fought both for and against the Fire Nation, he both helped and hunted the Avatar. During the course of the series his main goal was just to see Zuko being truly happy. Saying that he was unbiased makes it appears like that he thought everything he did was universally and absolutely correct, while he made it very clear that for the most parts of the series he changed his attitude for Zuko.
Iroh wasn't passive either. Ozai and Azula were aggressive and wouldn't hesitate a second to show their superiority over other people. Iroh wasn't like that, however he wasn't passive either. He just restricted himself to the least amount of power necessary and always attacked on the ideal moments. He was simply more patient, it shows how tactical he thinks, always abiding the right time. Saying that he's passive gives the impression he is afraid to do anything.
Your description is simply not correct, so trying to invalidate it consequently is quite pointless. Iroh wasn't passive, morally good nor unbiased to begin with. Those are your words, not his.
"She's crazy, and she needs to go down."
βIroh speaking to Zuko about Azula.
I understand that Azula was more influenced by her father than her mother (Ozai was proud of power naturally) and considering she never inherited any of his genes (not her birth father) the only thing wrong Azula ever did at the start was being naturally strong- that was it. Uncle Iroh crosses paths with her a few times but is so instantly determined that she is a lost cause. Why?
Not her birth father? Both Azula and Zuko are 100% blood relatives and the children of Ozai and Ursa. Azula however took more after Ozai, Azulon and Sozin, while Zuko then took after his mother and avatar Roku. This wasn't just a matter of influence as it was already shown when they were kids how different Azula and Zuko were. They didn't became like that due to influence, it's the exact opposite: because of how they were, their parents spent more time with one than with the other. At one point Azula said her mother thought she was a monster. Well yeah how come? Because she was one. Already when she was a kid acting like a cruel bully and talking about monstrous things, clearly to the dismay of her mother, however she did not bother whatsoever to change to gain Ursa's affection. This is something Zuko tried to do for nearly 3 seasons: gain his father approval.
The series itself explains this difference in personalities: destiny. Zuko was more of the Roku line, while Azula was more of the Sozin line, but because Zuko tried to be like Ozai, he started to get emotionally conflicted. This wasn't just about Azula being strong, her personality from the get-go was simply messed up showing no signs whatsoever of ever changing till almost the end of the series. You make it appear like that Iroh at one point made the conscious decision of I will only involve myself with Zuko and ignore Azula. That's completely wrong, Azula's personality, that's very similar to Ozia, pushed Ursa and Iroh away. Iroh said it at one point against Zuko: "I don't think you know my brother as I do" or something along those lines. He knew how Ozai was and he knew that Azula looked a lot like him and he also knew that Zuko was different from the both of them. Iroh sent Azula at one point a doll...and she burns it. While Zuko showed genuine care for his cousin, Azula was practically glad he was gone. Azula pushed people like Iroh and Ursa away, while Zuko attracted them. So there isn't really anything about Iroh siding with Zuko.
Also what was the most important event in Zuko's life? The Agni Kai with his father, where he was beaten down, scared for life and exiled. He even admitted this beating was in fact the best thing Ozai ever did to him. And what did Ursa say? That he loves him because he is doing his best, even when he gets knocked down or something like that. And when did Azula started flipping? When she started to get beaten down herself, when she wasn't winning anymore. This even caused a rift between Ozai and Azula, the latter even saying she did not want to be treated like Zuko. This pretty much sums it all up. If you want to see this as a 'choice', then it was Zuko who chose Iroh, while Azula chose Ozai. And thus, in a very twisted way, Iroh's comment of 'she needs to go down', was probably the thing Azula needed if she ever wanted to truly change. If she had been beaten a few times when she was younger, just like Zuko, she might have become more like him.
This makes all the difference in the world. Zuko accepted that he could never become the person Ozai wanted him to be and he 'chose' his mother and Iroh after having a long internal and emotional struggle. Azula chose to be like her father, but she couldn't accept that her mother might have seen here as a monster because of it and this caused likewise a severe emotional struggle when she started to lose and unlike Zuko she couldn't cope with it, but she didn't shown any signs either she wanted help unless maybe all the way at the end. Why would Iroh help her if she would just pushed him away? Or worse? Iroh didn't walk by and said 'I pick Zuko'. Azula her entire life she pretty much shunned Iroh, which she saw more as an obstacle than as a family.
She was in a similar state to Zuko morally at the beginning of her introduction and her breakdown that ensues later due to her mother issues is something that would've likely happened to Zuko if he was shunned by his uncle. Iroh believes that people can change and do good and yet he didn't have a single second of sympathy for the girl?
And it's not as if she was at any point an absolute unredeemable monster- her character in her youth showed signs of elitism but was still friendly even. Her mother never had time for Azula and from what we saw in flashbacks mostly spent her time lecturing Azula. Zuko was weaker and so got special treatment from their mother which forced Azula onto her father, forcing this terrible maniac as her role model. I'm not saying she's a saint, i'm saying she could've been saved.
She wasn't, she wasn't even remotely in a similar state as zuko when she was introduced as. Even though it didn't became immediately clear as what kind of person Zuko was from the very first moment, already during the very few first episodes it became apparent that there was more to him than just being a 'villain' and during the course of all three seasons he continuously changed. Azula however did not change at all till Mai and Ty Lee betrayed her at the Boiling Rock. Fact is Zuko and Azula have never been the same. Azula had everything, while Zuko had to struggle all the time, even long before the moment the series started. How Azula was at the end of the series is probably the closest she ever was to how Zuko was at the beginning.
Again Zuko, during his entire life, moved towards Iroh. Azula did the opposite. Yes Iroh believe people can change, but he also believes that that means they will change. This is clearly indicated by the feelings he has for his brother. Iroh did not shun Azula, it's the opposite: Azula shunned Iroh. Why would Iroh need to bother with a person that clearly does not want to be bothered by him nor wants to listen what he has to say? Azula made on more than one occasion clear how she thought about Iroh: an idiotic old man. When Zuko betrayed Iroh and Iroh was in jail, it was Zuko that kept coming to Iroh even when Iroh didn't utter a word. It was Zuko himself who came to conclusion what he was doing was wrong and searched for Iroh for forgiveness on his own accord. Zuko approached Iroh, while Azula shunned him. You are making it again appear like that Iroh suddenly decided one day to decide whether he wants to help Zuko and ignore Azula or the opposite, while in fact it's something that has grown during the years and where mainly Zuko and Azula were holding the initiative.
Again Azula already showed when she was very young to be much like Ozai. There aren't much flashbacks to give a clear analysis of her her relationship with her mother, but Ursa was lecturing her because of her cruel and twisted behavior, just like Ozai lectured in his own way how Zuko was a failure. And what did both of them do? Zuko tried to become the person his father wanted him to be, but there is not even the slightest indication Azula tried to be the person her mother wanted her to be. Even though zuko is older than Azula, while he was crying for his cousin and uncle, Azula was only thinking about how the chances of Ozai (and with extension her own) becoming Firelord increased, while Zuko was playing like a child with the dagger he was given, she burned her doll. Ursa did not push her towards Ozai, Azula herself searched for Ozai and it's that that pushed her away from her mother. Zuko tried to approach Ozai, so why couldn't Azula have done the same? You are placing the responsibilities with the wrong people. Azula did not want to be 'saved' and it's that that alienated her from her mother. If Azula had shown some compassion, if Azula would have tried to be friends with Zuko rather than bullying him, she might have become differently, but she herself decided not to do that.
Now that I read it like this, I would say that Azula and Zuko have had the exact same evolution, only in opposite directions. How Zuko was in the beginning, resembles how Azula was more at the end and vice versa.
In the episode 'Prayers of Ember Island' we follow the Fire Nation teens in their escape to a temporary social life, the treatment of Azula in this episode is VERY strange. She has moments of being her usual manipulative self but she also treats many of her comrades as actual friends for once. Sincerely apologising to Ty Lee for making her cry and admitting she is jealous of her. (WHAT)
She is open and mature with Zuko when he is ranting about his life, asking him who he is truly mad at and whether it's her. She also shows many attempts at fitting into a normal, friendly life- her upbringing ultimately failing her, but she TRIED. This episode clearly shows she isn't the monster the plot needs her to be, there's clearly a lot more there. She's a sympathetic character and one that strongly needed help, but unlike every other character never received it.
I don't think you should search too much behind those scenes regarding Azula. This is something pretty much everyone must have seen when being in school. Certain people hang always around other people, while you can clearly see they are not real friends, still they hang out. Why? Because they don't want to be alone or for other reasons, like fear. What did Mai say at the Boiling Rock? That she loves Zuko more than she fears Azula. That latter was absolutely not necessary to say, but still she did it. Azula even responded on it that she should have feared her more and Ty Lee knocked Azula out because she was very well aware she would potentially kill Mai. Also when Azula tried to recruit Ty Lee, the latter refused. And what did Azula? Pretty much threatened her with death. Mai and Ty Lee are probably the closest thing to what Azula ever had as friends and she had a certain affection for them, but it was still something very differently than what you would understand under real friends. Saying that she considered them as being elite faithful subordinates would probably be more accurate.
Azula had her own demons to struggle with, but she didn't receive help because she didn't want it and she didn't want to accept either that she needed it, hence she lost her mind. Even during all the event on Ember Island it was obvious that in the end it always had to go her way. She couldn't stand it that someone stood out more than her and when she gets a boy attention, even though it was meant as something comical, she proclaims they will become the strongest couple in the world or something.
You are placing all the responsibilities with other characters, that she didn't receive any help from them and that's because she became a monster. That's wrong, she is the one who pushed everyone away, already from an extremely young age she placed herself at the top of the world and looked down upon everyone and anything. As a result she obtained certain emotional problems, but she refused to cope with them. It's her own fault she didn't receive any help.
Conclusion: your description of many characters is wrong and then consequently try to proof that they are not like that. You place several responsibilities with the wrong characters and you are switching the cause and results of certain events with each other.