And I think it is simply, absurdly wrong to say that Azula does not 'really understand fire itself'. There's an ancient 2009 Avatar fanfic called Object Lesson with the premise of Azula ending up, Somehow, as Aang's firebending tutor, and to teach the outlook she swipes Katara's amulet and poses a question to him - suppose I threw this into a locus of any of the elements? What would happen? If I threw it off a mountain into swirling wind, they would carry the necklace until it fell back to earth, unharmed. If I threw it into crashing waves, it would be tossed by the currents for a while but if you dived down to retrieve it, it would be unharmed. If I threw it into a rockslide, it would tumble and bounce between the rocks but eventually scatter free, in all likelihood unharmed due to being too small and tough to be damaged.
And if I put it into the flame, even only partially, it would be consumed. It doesn't matter what the fire wants or how far into the fire I put the necklace, fire destroys. That is the nature of fire.
This outlook is not wrong. Yes, fire can be nurturing and life-giving, we all understand the value of huddling around a bonfire to ward away the night and the terrors it contains. But that doesn't mean you touch the bonfire. Even as a nurturing force, fire is still a thing that must be controlled and restrained, or it will burn you like any other fuel. Azula knows this, she knows all of this; the festival scene in loop two wasn't a revelation about the nature of fire, she knows it can be beautiful, it's simply knowledge she avoids bringing to her father's attention because it has no bearing on who she can be in his sight. She's an athlete, not a philosopher; she doesn't spend her time ruminating on the spiritual nature of fire, because she's too busy living it.