The culture of the Academy can be defined in two general ways, with one being by the Factions that hold power over the establishment and the "External Factors" that shape who can attend.
During the time of the first Exousia, those in attendance in Curse Academy were all users of Curse Series Wrath, Pride and Greed because of the Alliance between the respected Sins that were allied at the time.
In the time RE:Alternative occurs, the world is in a cease-fire of sorts, with Curse Users being more similar to Mercenaries rather than members of a royal court or anything of the sort. Many who attend the academy do so hoping to become nobility or set themselves apart as one of the best to become respected agents for a Sin and perhaps join their "Royal Court".
Curse Academy now is regarded as "THE BEST" school for combat and Curse Series mastery as all attendees are those with some experience of combat (Via Prior Schooling of sorts) with some having mastered their Natural Born Curse Series and learning new forms of their abilities based on the perspective cultures they may interact with.
Due to the Superbian Culture that surrounds the school, the requirement for excellence above all and merit have grown to radical terms. Many students turn up dead with secret dealing and "Accidents" in sparring matches. One's power and influence is determined by their legion, as one's power will naturally attract people around them. Good examples of this would be Zephyr being surrounded by other underclassmen that were members of his legion that went on to becoming Exousia of their own.
Classes are formally taught by distinct members of the Exousia due to their power and knowledge due to their legions. They may also designate members of their legions to teach as well if they believe said member is suited for such a task.