system
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human
[ATLA] Why doesn't Azula break out of the ice when she's trapped by Katara?

In the finale, Katara encases both Azula and herself in ice, then melts it partially so she can chain up Azula. However, it should have been easy for her to escape. Zuko was able to blast apart the ice ball Katara trapped him in and even melted through a thick sheet of ice when he was underwater. And this was all done in a cold environment detrimental to firebending. 

So why couldn't Azula break out when she was in the Fire Nation and had a massive power boost from Sozin's Comet? I would have expected her to blast apart the ice in an orb of blue fire, not be helplessly trapped and chained up.
gpt
Reason 1: the instance you mention of Zuko being trapped by Katara didn't include Zuko being completely enclosed in ice, but just being inside of a big hollow ball of ice. We know this because Zuko has both the space and air to taunt Katara while being inside of the ball. This is very important since we know that both movement and breathing is very important in firebending, not being able to move at all or even breathe (like Azula when trapped by Katara) is a big problem for a firebender.

Reason 2: already mentioned by another user, Zuko spent more time dealing with firebending in cold weather, Iroh even reminds Zuko to rely on his breathing for heat before he goes to capture Aang in that episode, suggesting that Iroh also probably trained Zuko in cold weather firebending techniques. We know Azula is a prodigy but for all we know she never even went to the water tribes in her life, cold weather techniques may be unkown for her.

Reason 3: Azula wasn't in her prime at the moment, maybe she knew a way out of the situation but her state of mind didn't allow her to think of that.