@pmntamp:
Arel's father's class / profession / rank is a "magic king" (or so) - which is the highest know tier of magic classes / proffessions / ranks.
Arel was trained by him for a while, right?
Arel has no class/profession himself, so he learns far slower than those with a specific class/profession.
But in exchange he has no restriction as to what he can learn.
The story's premise is that Arel compensates the disadvantage of having no class/profession by simply putting more effort and work into his training.
Add to that he also is actually a genius at anything he does.
Hence he "compensated" the years of training probably 1-5 hours a day with waiting for natural mana regeneration that normal people do in their childhood by simply training up to 24 hours a day for half a year in order to increase his mana pool - read chapter 14 - by drinking excessive amounts of mana potions to restore his mana whenever it ran out.
Then he learned the magic runes and their meaning from his father and memorized all of them - because he is either a genius or simply because he is the MC.
For the same reasons he then also learned in almost no time how to use the runes effectively to form spells in his mind.
Compared to that normal people with a magic profession have a skill-like intuition/inspiration how to form the spells by having the complete spells simply appear in their minds.
This difference means that normal people do not actually understand what part of their spell has what effect on the magic - they just know "This spell will have this fixed result." while Arel knows exactly which runes and their combinations in his spell have what exact effect.
Therefore Arel can cut out unneeded parts of the spell or adjust the spell to change its power, its range or/and its area of effect while normal people cannot do that.
So with his mana pool being insanely high from his non-stop training for half a year, knowing all runes for all elements from being taught by his father and being able to adjust any spell to suit the situation he is in means that Arel is actually far beyond the basic level of any new student who have just started learning to use magic at all.
In order to learn more about magic and to be recognized as a capable magic user despite having no magic profession Arel decided to join the academy of magic.
But as explained above he is already far beyond the basic teachings.
In order for him to learn new stuff he needs to reach the advanced classes where you are teached new spells and the like.
Yet a school cannot simply let someone go to an advanced class without having confirmed that the person is good enough for that.
However allowing anyone to ask for a promotion whenever they want would lead to many students who overestimate themselves to ask for the promotion exams - this would obviously result in almost everyone failing the promotion exams and create unneccessary work for the school.
So they put heavy conditions on taking those promotion exams ahead of the regular schedule.
Arel has been working on fulfilling those conditions and taking the promotion exams for these last few chapters.
And now he finally finished this part... at least for going from classes for year 1 students to classes for year 2 students.
The question is if he will be content in classes for year 2 - which I doubt...