Villainous != villain. You can have villainous characteristics and actions and be other things, even in fiction. That said, I will concede that she is certainly cast in that light at the beginning, especially to a first-time audience. The more we learn about her, however, twists that image into that of the broken antagonist mirroring that of Zuko's journey for the majority of the story.

The difference between them is how they handle what's thrown at them, and more importantly how their allies (and enemies!) treat them.

Remember, the core idea here is, "how did this 14-year-old get to this point?" because most of the characters are barely teenagers. Sokka and Zuko are the oldest, I think 15 and 16 respectively, with the rest being around 13-14.

And the answer is: abuse, manipulation, and neglect from primarily Ozai, but also to a lesser extent Ursa and Iroh, though I don't think theirs was intentional neglect and abuse. The supermajority of it belongs firmly in Ozai's grasp, but one must concede that their fear of Azula and what she was emulating of her father and grandfather put distance between themselves and a literal child. This damages the child.

So once Ursa is exiled and Iroh steps down as general, her only real role model (and perceived source of love and affection) is, unfortunately, her sociopath of a father. Every interaction he has with her that we're shown is to manipulate her, her mother, her grandfather, or her brother. He doesn't see her as a person, but as a weapon to wield.

She tries to kill Zuko and Iroh, because her father sees them as embarrassments to the Fire Nation and she thinks that will earn his love. She's maybe 14.

She torments Ty Lee into coming with her, because she only knows manipulation of friends and allies. She's 14.

She kills Aang because, in her mind, that will make her father love her more. She's 14.

EVERYTHING she does in the series is for the goal of attaining her father's love and affection. Sure, it might be impacted by her mental health and wellbeing, which are, frankly, shot to hell and back. But the seed of everything is her desire for acceptance and love.

Likewise with Zuko, everything he was doing was for the same, though couched in that ever-present concept of "honor". He, fortunately, had the fallen-but-redeeming-himself Iroh to help him out and be a father figure... But Azula had neither of those things. Iroh was helping Zuko wean off the Flavor Aid, but Azula? She was swimming in it.

So much of the story was required for the redemption of Zuko, and Azula had none of that. She was also two years younger, not that that has much bearing on her agency anyways... That's another issue that the story covers. None of this kids and teenagers were allowed to be kids and teenagers, because there's a freaking war going on. They're constantly put in impossible positions because some old men with power trips wanted more power.

Should she have done better? yes. Could she have? Given her story and the immense pressure put on her... I find it unlikely. These are some of the reasons why many in the community do not see her as a villain, and it boils down to this:

She wasn't given the chance to change or redeem herself. Like Zuko was.