Miss Boudicca Battle-Axe is a school teacher and one of the secondary antagonists of the Horrid Henry books and TV Series. She teaches Horrid Henry, and many other students except Perfect Peter, Goody-Goody Gordon, Tidy Ted, Spotless Sam and Clever Clare.
Why She Sucks
For starters, her character design (particularly in the TV Series) is very mediocre and unappealing to look at, in fact, it's pretty much on par with MrCrooker from The Fairly OddParents levels of ugliness (except worse).
She once said that Henry's class was the worst she had ever taught all to spite her students, making her seem uncaring and selfish.
She once publicly humiliated Henry in front of the entire class in the episode Horrid Henry's Underpants. She shamelessly revealed something personal as a way to humiliate Henry instead of respecting his privacy, making her very annoying and sadistic in the process.
She dislikes the class she teaches for such petty reasons and she enjoys giving her students detention for no reason but for her own enjoyment.
She even gave Henry two detentions for just having an unpopular opinion on a TV show Henry thought was overrated. Making her look prejudiced and obnoxious for others to have their entitled opinion.
She always keeps an eye on Henry, even when he is not being horrid at all. This can get creepy and concerning when it looks like she's the type of teacher who targets one student for her own sadistic pleasure.
Hypocrisy: Though she catches Henry and Peter selling perfume on the school grounds and gives them double detention for that reason in particular, Miss Battle-Axe is still seen trying some perfume that Henry and Peter made which soon leads to her humiliation as seen below in RQ#4.
Despite being one of the secondary antagonists to Henry, she is sometimes treated like a protagonist for the writers to make us sympathize with her. While making a merely obnoxious character have something sympathetic and likable about themselves is a great idea to make them less hateable, it needs to have a right amount of balance for her actions and how much character development she needs to get to make her a likable character. This, unfortunately, fell apart after she becomes more sadistic, annoying (intentionally or not), and mean-spirited even after we see how she dealt with her own mom.
It is well-established that she dislikes Henry for the reason of being horrid at times.
The fact that she has an overbearing mother who greatly disciplines her, plus the fact that her students aren't exactly the most ideal students (Henry especially) can make viewers feel a little sorry for her. It can also be the very reason why she's paranoid and spiteful.
While disliking Henry mostly for his horridness in her class, she does occasionally do nice things for Henry.
She did praise Henry for saving his brother in the episode "Horrid Henry: Trapped" and she even brought him a somewhat wholesome card signed by other students. Even though Henry didn't really appreciate it due to how embarrassed he was over the circumstances from his situation.
She does sometimes get a level of comeuppance for her bad treatment of Henry. For example in the episode "Horrid Henry's Smelly Stuff", when she put both Henry and Peter in double detention after catching them selling perfume, she tries some on and when she sneezes, all of her hair comes off, leaving her completely bald where she covers her head with a book and runs out of the classroom humiliated.
She probably wasn't meant to be liked for being such a mean and strict teacher to begin with.
She at least doesn't physically abuse her students, unlike Miss Trunchbull or Dolores Umbridge.