This could be the 2014 anime Mahou Sensou.
one brother hates the other and also frames him for the death of their parents.
The main character, Takeshi, is hated by his brother, Gekkou, who becomes one of the series' main villains. Their parents are still alive (or at least, their mother is), but if I recall correctly, they had a sister who was killed in a car accident - their mother blames Takeshi for the accident but (again, IIRC) it's eventually revealed that Gekkou was in some way responsible and had framed Takeshi.
There is a school for people with special power which first the main character declines but joins.
Takeshi and his friends become magicians in the first episode after coming into contact with a group of villainous magicians, and subsequently enrols at Subaru Magical Academy, a school for magicians. I don't remember whether he initially declines.
(If it is Mahou Sensou, then a) it's a duplicate of this question, and b) I must advise against re-watching it because it's extremely badly-written.)