Okay, as it seems no one's gonna do it, then I'm gonna do it!
Let's talk about Ursa's relationship with Firebending...
... more specifically, her relationship with her Firebending children.
Starting with a question: What does being a Firebender means to Zuko and Azula?
In The Search, Ozai says this:
Had Zuko not become a Firebender, Ozai would've got rid of him, perhaps have him banished, since he was a fan of doing that back then, but he could also have him killed, we all know Ozai has no qualms when it comes to kill children.
For Zuko, Firebending means survival.
So when Ursa shows him support, when she encourages him, when she pushes him into keep trying, even when it's hard, specially when it's hard. That's not her "playing favourites." That's Ursa assuring his survival!
Ursa needed Zuko to be a Firebender, because she knew, from the day he was born, what it would mean for him not to be one!
Then we have Azula. She was "born lucky" she had the said "spark in her eyes." Ozai was sure she would be a Firebender from the moment she was born and she would be able to fulfill his plans for her, unlike Zuko, who at that point was older and had grown to possess that "odd affinity for the weak" he mentions in The Promise:
Ozai had no interest in Zuko anymore, Firebender or not, he knew Zuko could not be shaped into what he wanted. Which automatically means all his attention now shifted towards Azula. If Zuko couldn't be Ozai's weapon than Azula would.
For Azula, Firebending means to become a weapon.
When Ursa saw Azula Firebending, she saw the exact moment she lost her daughter. When she reacted with fear and disappointment, it wasn't because she "didn't love Azula." It was only that her hopes were crushed.
Ursa hoped Azula wouldn't become a Firebender, because then she would be save from Ozai, because then Ursa wouldn't have to watch her own daughter be turned into her abuser, the actual person she fears!
That's just how complicated Ursa's relationship with Firebending is. Its presence in her life is always rooted in fear. Fear Zuko won't Firebent, fear Azula will, fear of what Ozai will do in any scenario!
The way her son's life depends on it, just as much as her daughter's life will be entirely destroyed by it.
Fire to Ursa is nothing but fear! So how was she supposed to react any other way?
Ursa is not proud. She's not happy. She's terrified. She's mourning the daughter she could've had. She's coming to terms with the fact that no matter how hard she tries, her influence will never be as strong as Ozai's. Because if even her own life is under Ozai's total control, what can be said about Azula's?
