sympathize means having understanding for someones misfortune or sorrow, and Azula doesn´t display these because she, for the most part, is unaware of her own emotional faults. She ADORES her father, who emotionally manipulates her by coddling her. Then you could argue that this might have some moral lesson for real life comparisons.
Which actually is true, if you know some or other about childhood psychology
What you mean is that Iroh should have EMPHATISED with her, and tried to correct her course, which is something you do as a viewer do as you explore her character. But Iroh doesn´t have the insight the viewer has, and he only really had it for Zuko because of that hole his dead son left in him. So the entire postulate is bollocks
Whats happening is that people in this thread are trying to hoist the faults of Azula as a person onto another character, based on your omniscient awareness of the whole storyworld, instead of seeing her as a character through the existing dynamics as shown in the show. No one knows whats going on inside other peoples heads and can´t fix problems if they don´t manifest and they have rapport to act on it. This is true for real life, and good writers knows how to write this into their fiction