Because apparently I don't ship anything that the majority of any fandom approves of.
Aang does not love Toph; he loves the Blind Bandit, the part of her that is rough and tumble, stone and steel and reckless danger, the earthbending master who can see with her feet, who swears like a drunken sailor, and who moves to reverberations in the earth even the Avatar State cannot fully understand. He loves how fierce she is, how uncouth and vibrant and refreshingly alive she can be, how she doesn't care one whit that he's the world's spiritual protector, the living embodiment of everything precious and powerful when it comes to bending.
But he also knows that is not the whole of Toph Beifong, knows that there are hidden depths to her, hidden faultlines and fractures coursing through her soul, and he knows he does not truly love her in the vast, heady heaviness of the word. It would be more accurate to say, perhaps, that he loves her like a sister; he will stand by her to the end, die for her, but she can annoy him in ways Air-Temple trained monk should be able to handle, and there are times when he would rather she was exactly where he wasn't.
He knows she has imperfections, as does he and everyone else—everyone else? A lie, and he knows it, too—and while he has accepted them as simply part of who Toph is, he does not find all of them endearing (a monk such as he does not appreciate the way she abuses language like Katara does Zuko). She is a friend, a close friend, his earth-bending sifu, and yes, in many ways the sister he never had, but he cannot imagine living with her for the rest of his life, going to bed with her and waking up with her and sharing meals and family and children.
They just wouldn't click. Earth and air—so what if he's the Avatar? The sky is his home, and it will always will be—don't mix; they wear one another down, blunting, eroding, their very natures always working against one another. Aang and Toph, Toph and Aang, they would not—could not—work. Even if he loved the whole of her, and not just the part that appealed to the rebellious child he once was, the part of her that did everything he wanted to but couldn't, in the end whatever was between them would crumble and fall to dust.
Aang does not love Katara; he loves the idea of Katara, peace and happiness and a soft sort of joy that reminds him of life back at the Air Temple, when he was young and actually had time to be a child rather than the Avatar. She is calm and gentle, a balm to his wounded soul, cool and reassuring like a river's gentle caress—he knows it's practically a tautology to compare a bender to their element, but that doesn't make his comparison wrong—and he knows that he would find almost everything he wanted in her arms.
The operative word being almost.
Katara is beautiful and kind and safe, every part of her a subtle almost-perfection that would fit him in a way the title of Avatar still doesn't… if he was anything like he knew he was supposed to be. The problem with who is is, however, Aang thinks, is that he does not want to be safe. He is an airbender, first and foremost – yes, airbending is defensive, redirection and evasion rather than brutal counters, but it is not constrained.
Airbending is freedom, wild and fierce, and the first thing he ever truly understood. For an airbender, safety is an illusion – for all its vaunted pacifism, it cannot heal, and it cannot truly protect anyone else other than the wielder. Airbending is, in fact, in many ways the most dangerous of the bending disciplines.
After all, it does not matter how much water you can control, or how many boulders you can summon, or even how much lightning you can hurl, if you cannot breathe.
It is his most desperately-kept secret, and truth be told he wishes many a time he hadn't discovered the possibility, but there is a tiny, tiny part of him that studies everyone he knows and marvels at how easy it would be to suck the air from their lungs and watch them choke to death. There is a monster in everyone, sometimes on the surface, sometimes hidden somewhere deep, but the Avatar's problem is that his monster is so much more dangerous than anyone else's.
That is part of the reason why he cannot truly have, or love, Katara. She is a warm blanket on a cold winter's night, a soft embrace in the middle of a funeral, and not for him. She has power, but she is not powerful (not because she is weak, but because water is not an element that demands dominance, rather acceptance), and he needs someone who is capable of staring into his abyss and not flinching; Katara is another of his closest friends, but even she would shy away from the horrors he knows he is capable of.
Aang does not love Azula. Or so he tells himself. She is the enemy, primal, fierce, dangerous in ways he cannot imagine—a lie, he was once Avatar Roku—and she would kill him if she could (she has, once, but he is the Avatar and even death cannot conquer him).
She is not as beautiful as the sunset, or as mysterious as the stars; those statements are simply wrong, wrong in the way it would be wrong to say fire needs oxygen to survive, or that the wind can fan the flames as easily as it can put them out. Her eyes are golden; they cannot glint like lightning in the darkness, vibrant and energetic and so very, very alive. Her hair is black as sin because she is sin, and he should not be attracted to her.
There, at least he's not lying now. He said should not, after all, not isn't.
He just can't help himself. He understands her in ways the others cannot; they see her and judge her as a horror, a perversion, while he knows the only difference between them and her is that she is not afraid of the monster. It does not help that she is startlingly attractive, wicked and wickedly curved, or that she is a once-in-a-generation bender, a prodigy beyond even Toph, because whereas Toph is a genius born from necessity, Azula is simply a genius born.
There is something glorious about the way she fights, rigid control and a sort of icy fury that should not come from such a volatile element; he would deny it if he was ever asked, but when he fights her he does not take the easy way out, because he craves the thrill, not the thrill of combat or adrenaline but simply the thrill of Azula. Sometimes, he thinks she might know as well, and if he sometimes wonders how she could come so close to killing him without quite connecting, it does not matter because the truth of they is a forbidden thing.
That does not make it any less wanted, of course.
Where Toph would annoy, Azula would wait. Where Katara would reassure, Azula would challenge.
Where Toph has imperfections, Azula would be—is—perfect.
Where Katara would flinch, Azula would embrace.
There is perhaps one thing he can take out of their situation, one fact that reassures the hidden parts of his heart: Azula craves strength, strength and power, and she has both in extraordinary measures. She would not submit to any man who could not defeat her in single combat, and there are precious few in this world he knows who could, bar him – her father, her uncle and probably his old friend Bumi. And none of them would want her in the way he does.
So she is his, for now, even if it cannot ever be.
When he kisses Katara, on the eve of battle, it is the final nail in the coffin he had been struggling valiantly to keep open. There is no spark; she is soft and pliant and everything he imagined his first kiss to be, but that does not change the fact it not is everything he wanted it to be. It is the difference between thoughts and dreams, reality and fantasy, and the part of him that will always be a monk notes that his heart has made the decision his mind will not.
And so, when the war is won and Zuko is the Firelord and the world is restored to balance, he embraces the chaotic turmoil in his soul.
Her smile, when he opens the door to her cell, is a vicious, brutal thing, all sharp edges and sadism, and so purely Azula that he cannot help to smile in return. It's foolish and wrong and forbidden, but he can read her like nobody else can, and for the first time in her life, the fact her smile does not reach her eyes is a good thing.
Her bonds snap, and he offers her his hand; she does not take it, and it is in that moment that he knows she might be broken but she will never be extinguished, and he loves her for it. He does not think she loves him in return—he does not think she can—but she cares for him as best she knows how, as best the trueborn daughter of Firelord Ozai ever could – by acknowledging him as her greatest enemy.
It is why she never takes her eyes off him, and when he kisses her for the first time, there is fire and lightning, and not only from her lips; she might be letting him closer than she'll let anyone else, but she will never let him take advantage of her.
But he is the Avatar, and he does not fear her. And that is why she will stay.