I’m glad someone brought this up because it’s an aspect of Azula that’s rarely discussed. Many might be confused by her actions in the comics, but what she does makes sense because, after years of indoctrination, she believes that an ideal ruler for the Fire Nation should embody the values she was taught: someone with control and power over others who also uses fear to keep them in check, that’s why she encouraged Ozai to take Azulon’s place and why un the comics she wants Zuko to become like Ozai.
While many argue that Zuko was also subjected to the same propaganda, it’s important to remember that he spent more time with Ursa and Iroh because Ozai dedicated his time to training Azula, whom he saw as his heir and, above all, as his best general in the future. Furthermore, Zuko was exiled from the Fire Nation, where he was not only shielded from the Fire Nation’s constant propaganda but also forced to live alongside other cultures that had fallen victim to the Fire Nation. Azula, on the other hand, didn’t experience this because she only went out on missions, dedicated to completing them, and immediately returned to the Fire Nation once they were finished.
Moreover, the reason Azula takes loyalty seriously is because loyalty (especially loyalty to her country) is one of the values she was taught. Therefore, she took Mai and Ty Lee’s betrayal very badly, it wasn’t just a betrayal that caused her to lose the control she had over them as friends, but by betraying her, the princess of the Fire Nation, they were also betraying the Fire Nation itself.
If we consider Ozai’s conversation with Azula before leaving to conquer the world, in which he entrusts her with the Fire Nation, it suggests they likely had similar conversations combined with Azula’s statement to Long Feng that power is innate, not acquired, it implies that she probably had conversations with Ozai where he emphasized that, as not only a talented firebender but also his heir and the princess of the Fire Nation, she bore a greater responsibility and commitment to the nation’s well-being than the average soldier, making her incapable of seeing herself outside of that role. It’s like Uncle Ben said in Spider-Man: “With great power comes great responsibility,” but executed in an extreme and toxic way for the convenience of a war regime.
Azula is not just a girl who had toxic tendencies that were encouraged by her father and his inner circle and redirected those tendencies towards a political cause, but she is also something much more terrifying: a child soldier who gives everything for her country, a true patriot.