So, everyone has discussed this to death and Katara is more than proven within the show to be able to take down Azula, mentally stable or not. But OP made a very serious accusation that I feel I have to address.
“…Azula only lost to Katara because of plot armor”
You know what? I’m gonna let Piandao have the stage from here:
“…your weapon is an extension of yourself. You must think of it as another part of your own body.”
“…You must learn to use your sword to stamp your identity on a battlefield. Remember, you cannot take back a stroke of the brush, or a stroke of the sword.”
Oh, and look at Katara, all sparing Azula’s life without spending 5 episodes of preachiness about it! She could have let her drown. She could have stabbed her with an ice dagger. But she didn’t. Do people talk about this? No. It’s all about Aang and his lack of character development.
“Landscape painting teaches a warrior to hold the lay of the land in his mind. In battle, you only have an instant to take everything in.”
“Rock gardening teaches the warrior to manipulate his surroundings and use them to his advantage”
Katara uses her element like an extension of her own body, she is able to quickly survey her surroundings and take advantage of them, all the while considering the implications of her actions and choosing whether to take a life or not.
@trapcard, everything is a plot forwarding device. This isn’t real life. Not a single stroke of color in the show is there by accident. Every element, every word, every decision anyone makes through 61 episodes is intentional and there to further the plot. Azula has a mental breakdown. That is her character, that is her arc. Katara has canonically bested her twice, both when she was stable and when she wasn’t. In this fight, we see Katara being the epitome of a warrior the way Piandao has framed it - fluid, creative, fast thinking. And more importantly than anything else - she makes her own decisions, taking into account her surroundings and options. She doesn’t let them make the decisions for her.
You know what a plot armor actually looks like?