Izumi Curtis is one of the most strong-willed and intimidating female characters in all of Fullmetal Alchemist, rivaled only by Olivier Armstrong. Born in Western Amestris, Izumi set out when she was eighteen to try to find a formal teacher to advance her studies in alchemy to no avail, and then decided to set off on her own self-taught travels. One fateful stormy day in Resembool, she'd stop to use her alchemy to help keep the town from flooding, where she comes across Edward and Alphonse Elric.
There are many strengths that make Izumi a great teacher for the boys. She is strong-willed, soft underneath her intimidating exterior, and understands how heavy the toll of committing taboo really is. However, that doesn't mean that she is the perfect candidate to be teaching kids, and has points that make it arguably difficult to claim her as a great role model through-and-through.
10 Great: Healthy Beliefs
Although Izumi is an incredibly capable alchemist, she also still believes in the value of doing things with one's own hands, if that's still a possible option. It's unsure if this is something that she's always staunchly believed, or if this is a belief system that she developed after her rebound with human transmutation.
A small child from the village comes to Izumi, asking if she can fix his broken toy "with alchemy." Instead, she takes it in her hands and fixes it the traditional way instead, instilling how important it is to not rely solely on alchemy.
9 Not So Great: Overly Violent
It's one thing to harshly reprimand one's students when they do something wrong, but Izumi takes this to an unhealthy extreme a lot of the time. Sure, in the early 2000s, female characters being overly violently aggressive - especially towards the protagonist when they do something foolish - was a trope, but that doesn't mean it's one that makes for a good character trait.
Whenever Izumi rushes in to save Ed during his fight with Greed, she completely pummels him in the process. She is seen doing similar acts throughout the series that make her come off as physically abusive at worst.
8 Great: Adventurous Spirit
Izumi is incredibly fearless and self-reliant, able to survive in the harsh Briggs Mountains by herself for an entire month, and she has an affinity for traveling. Until she met her husband and decided on wanting a child of her own, Izumi was an unbound free spirit who traveled wherever her adventurous spirit would take her.
This is a great trait that she actually seemed to have passed on to Edward, given how fearless and excited he becomes about exploring new places during his own travels.
7 Not So Great: Death Threats
Going along with her more violent physical tendencies, Izumi has an incredibly bad habit of threatening - and actually at times endangering - the lives of her students, particularly Edward. After learning that they had committed a taboo after studying under her, she rejects them as students and chucks a knife directly at Ed's head when he tries to re-enter. They're even warned by her husband not to let her kill them, which isn't stated in a joking manner.
Ed and Al are also seen essentially having a panic attack upon thinking about visiting Izumi for the first time since the accident, fearing her reaction. Winry's remark that they should "find a new teacher" is played off as a joke, but it's a genuine sentiment given some of Izumi's reactions.
6 Great: Emotional Support
The Elric brothers have a tendency to shove many of their emotions aside, especially when it concerns the taboo that the two committed. It makes sense, then, that Izumi would naturally be the one who could empathize with them the strongest, as she also was driven to commit the same act to try to revive a dear loved one.
They tried to insist that they were fine in front of her, but she relents, stating that it's okay for them to hurt. They break down in her strong familial embrace, and it's an incredibly heartwarming moment that really shows their bond.
5 Not So Great: No Contact
Whenever Ed and Al lament over the thought of having to give a visit to their old teacher, it's mostly due to the fact that she still doesn't know they committed the taboo. Considering Ed had been a state alchemist for several years at this point, it does beg the question of why Izumi didn't try to contact them.
While Amestris still lacks modern-day instant methods of communication, it isn't like she couldn't have tried sending out letters. In fact, when they do show up, at first she seems much more concerned with pummeling them than asking how they'd been holding up.
4 Great: Away From Taboo
Because Izumi had already made the mistake of committing the ultimate taboo and suffering the harsh consequences, she understood full well what Edward was thinking when he first mentions it around her. She immediately snaps, stating that it's forbidden, and something that no self-respecting alchemist should dare to try.
It's clear that there is a personal reason why she felt so strongly against it, though it's not explicitly explained until much later. Sadly, Edward is smart enough to hide it after this so she can't stop him.
3 Not So Great: Overly Harsh Training
Izumi is no stranger to strict teaching, as she was told to survive a month in the harsh Briggs Mountains by herself. This seems to be something that stuck with her, as she later dumps Ed and Al on an uninhabited island and tells them they must survive for an entire month, or she'd refuse to train them.
It's one thing to put students through the same experiences that molded their teacher, but Izumi was eighteen when she did this, and the Elrics were only just hitting their double-digits. They did almost die, both from enemy attacks and starvation, so no matter what Izumi's intentions were, it makes her look like a less-than-exceptional teacher.
2 Great: Helps Those Who Can't
Izumi has a tendency to help others who have the drive, but perhaps not the means, to help themselves. This is clearly seen with how she agrees to take on the Elric brothers, as she outright refused several times before it was stated that they didn't have any parents. Izumi's empathy is reflected clearly in her eyes, and she then states that she doesn't have any other choice, since she'd feel too guilty abandoning two orphaned kids.
Izumi's kind nature is also shown in how she repairs the toys of neighborhood kids, while also instilling into them that it's better if they simply aren't carelessly rough enough to break them in the first place.
1 Not So Great: Wrathful Temper
Although Izumi is the most understanding when it comes to the Elrics' situation and the burden of having committed a taboo, she's also the most outwardly violent and furious towards them about it.
This instilled a debilitating fear into Ed and Al so deep that they genuinely considered running away instead of facing her once more, and they didn't even flinch when a gun was pointed directly at them. It doesn't take much to send Izumi into a blind, violent rage, which just doesn't help someone who's supposed to be a teacher.