[contains wha spoilers from manga]
Realizations after episode 5 with a dash of my opinions i guess.
Regarding the anime's episode 5.. we see Agott being so amazed after the dragon scene (this reason or another one later). I can't remember if the manga has it. But either way, it makes sense. I think Coco said that Agott's fave type of magic is similar to the water rose Qifrey showed her when she just arrived in the atelier...
...Then that means the dragon he made here is also that type of magic. Qifrey showing it to be used that way probably gave Agott so much inspiration and encouragement that her fave type of magic isn't just a cutesy-cutesy one. I mean it is cute, and beautiful but there's more to it aside from being decorative and pure entertainment. And other people were wrong to some degree (or just flat out wrong) for judging her to prefer that. Deeper into the manga, we have heavier proof of that, her knowledge in mimicking different living beings saved a whole lot of the population. It was the main trigger for her to accept what she likes. And Qifrey and Olruggio (mainly Qifrey) was using a water dragon again iirc as they distract the opponent while the others get ready for the final blow ahaha
But during this time in the anime, Agott probably realized, that you can't take that type of magic at face value. That creativity with it, beyond the artistic side, is what matters. Or maybe she thought of it that way since the beginning but was shaken up due to the adults' reaction, especially her mom's. She was probably convinced until Qifrey showed her how to use it differently or more creatively.
She kinda used it as a distraction during the river incident (which either how she's been using it all this time or she started getting inspo from Qifrey and use it as a signal, that it can be more than an entertainment. Which Dagda thought it was), while Qifrey actually used it for combat/disarming the opponent. In ep 5, it's to make the dragon unconscious but later on, he was able to use it to aid him in chasing someone, and lots of other ways. A lot of it Agott didn't see but you get the point.
In my opinion, mixing that kind of magic into what they have to do is actually helpful in hiding their secret. Agott used it, too to make Coco's product in the parade more appealing to the common people (the fish trail stuff). They could have simply added the "water send itself to a certain direction" kinda magic but adding that "simple" decoration made the magic more enjoyable to use, even the kids started wanting to do the chore it involves with.
The other reason why she was speechless was probably the change in Qifrey's demeanor from before and during him using magic to after the dragon passed out. Tho Agott was clinging to him in a way she won't see his facial expression so im leaning more into the first one. His serious tone of speaking might be considered into the mix of reasons but idk that feels kinda normal for a teacher + adult witch at work. Facial expression says more imo.