I think kids in America -- and probably the West in general -- grow up a lot more slowly than they could. I don't think this is necessarily a bad thing, but I do think it's a thing.
For the most part, American kids are not given any responsibilities and most of them spend most of their time in a public school system that is designed to educate mass numbers of kids, meaning that it needs to use standardized materials and can't provide individually-tailored teaching. The classes therefore move at the wrong pace for pretty much everyone -- too slow for some, too fast for others -- and the material is going to be uninteresting to most. This is before we even get into discussions of "teaching to the test", inappropriate subject matter, etc.
If you treat a kid like an adult, they will (IME) usually act like one to the extent that they are physically and cognitively capable of it. Also, effort matters far more than talent; when I was teaching, the student who wrecked the curve was by no means the smartest in the class but she was absolutely the hardest working.
Honoka and her peers are getting treated as adults. They are also students at an extremely selective military school, being offered the chance to enter the highest-status and probably highest-paid role in society. They are under military discipline, so there are clear rules of behavior and clear standards for success. Class sizes are very small and the country is strongly motivated to get as many ninja as they can, so it's possible to get a fair amount of individual attention. Add to that the fact that some of what they are learning will let them fundamentally reshape reality in ways that real-world kids literally dream about. (Granted, that's not the stuff that Honoka is officially doing; firsties mostly do academics, physical conditioning, meditation, military codes and behaviors, etc. Kagome has taken her out of that track, and she knows that if she works hard and learns the boring math stuff then he'll teach her how to blow stuff up and cheat and make stuff appear and disappear and generally be awesome.)