Let my start of by saying that I never was really a fan of the shipping ideas. Still, I was happy for Aang that he finally got to be accepted and willingly kissed by his true love (something he truly deserved after saving the world, in my opinion). Also, Zuko was quite happy, having Mai by his side and as his girlfriend. But this blog post isn't about who was happy and who wasn't. It's about why Zutara would not have worked out.
First from Aang's perspective: We all know that Aang had a crush on Katara from the very beginning of the series. It began to develop drastically especially after they had become friends and were on their once-in-a-lifetime journey. Aang had made many attempts to tell her, and ended up, being afraid he might not come back, kiss her before the invasion, an act Katara saw as "out of nowhere".
Now for Mai's perspective: She had had a crush on Zuko since she was a little kid. She was teased by her friends Azula and Ty Lee, although not for the same reason (Azula thought it ridiculous; Ty Lee was all for it). Zuko's side was unknown when he was a kid, but we can infer that he had feelings for her, too, seeing how fast they shared a kiss after they were reunited in Ba Sing Se (seen in the Lost Adventures comic).
Now from Katara's perspective: Katara is the person that could go both ways, seeing good from both Zuko's and Aang's sides. As you saw in the tenth episode (Jet), she fell in love with, what seemed to her, a mature, trustworthy boy that understood her. As we all now the beginning credits that tell you what has happened in Avatar so far are special, because they tell what has happened so far that will affect this episode, not necessarily what happened last episode. And when it was Jet's episode, you saw Katara being angry at her brother. This shows that she lacked that mature boy on her side - she lacked a fatherly figure. So Jet shows up and she is "all caught in his spell". Normal. And even though the viewer may not fully understand Katara's feelings, they overall "feel how she feels". I think this lack of fatherly guidance makes us think that Zuko would have been a better choice. But if you think about it, both he and Aang went through a journey that made them much more mature than most people we see in our everyday lives. I'll say this once again: Katara is the one person that could go both ways.
And now from Hollywood's perspective: We all know that Hollywood wouldn't break their main character's hearts. So how did people imagine Zutara would have worked out? As you can see up there, Aang would be heartbroken, Mai would be heartbroken, and Zuko and Katara have been told that they are in a girlfriend-boyfriend relationship. We've seen the reaction.
I would be thankful if you would respond, and tell me what you think of my ideas and reasons.