@Kraco - Leo, a 2nd division student, was beating up the terrorists quite easily. I'm sure the Vice President is stronger than him. I think you are having trouble about students being able to fight better than veterans. But that's the thing, the people in that school are raised to be fighters. Part of their curriculum is combat. They likely train or fight outside of school as well, especially if you are a from a famous family. They are very far from what you would expect a normal student in RL or other fiction. Tatsuya may be a super special case, but all the students are special. Some of them are better than others (Erika), but that does not mean the weaker ones cannot fight off a gun toting mercenary. They are the elites after all, as said in the first episode.

@Ryll - The problem with what you are demanding from the show is that it cannot be done. Most of the magic will always happen back end, and the explanations (if we even get them) will always be after. They won't be chattering around explaining themselves during combat like the usual shounen series. Some moves may be flashy, but most will simply be effective, and that is what I like about the combat. It is practical.