There are numerous times in the series Katara has really lost her cool; but really, those times aren't as many as people seem to believe. Specifically I am focusing upon Book 3. The first thing we see of her is her being rude to her own Father. "Why the hate?" Some must think. I'll just focus on that for this blog.
Weeks of Despair
She was being testy with him. She shouldn't have been, no. The series also didn't exactly show a lot of why she felt that way, but just left hints in places to imply what was wrong with her emotionally. Honestly I think part of this was for shipping purposes (to keep 'Zuko' open for viewers). Another reason was time...they didn't have the time to focus an episode on Katara's feelings. It just wouldn't be necessary.
Amidst all this pain and failure - the fall of Ba Sing Se and in turn the entire Earth Kingdom, hope was at an all time low. She didn't have normal hope. If you read The Bridge, it was Sokka who was full-on in belief that Aang would be alright, and Toph was nonchalant about it, not making a big deal. Katara, dealing with lifeless Aang firsthand, desired nothing more than to try to help him - but feeling his condition and her lack of changing it - teetered on the edge of despair. And here; she is reminded of her Mother. She had lost her Mother to the Fire Nation; now she had lost/was losing Aang. Her Father had come back into the picture; but having not had him in her life the last couple years - inclusive of all the battle and hardships she has had to endure, trying to keep everyone together and be the adult, she hurt with feeling that his leaving is what made her and everyone else suffer so much. Wondering if he really understood her, if he really cared that deeply/why he just left them to fend for themselves. (It's a good thing Zuko is the only one who raided the SWT during that time. They were at the FN's mercy)diary; not confiding in those around her. She's more broken during this time than ever before, and not one to show that she is broken... always trying to be strong.
Even though her mind and heart were torn; she could still take the time to see through this pain and understand the reasons for her Father having left, and keep herself from being fully furious with him. She loved him, but with everything that was engulfing her, she hurt, and pushed him away. Her being just fourteen definitely should be remembered here; as it really helps to make sense and show that she is just a child, trying to live as an adult. It's not an easy task for the heart...there definitely would be breaking points.