I think I've figured out the backstory.
His father is also the father of the council president. He's rich, obviously, and had an affair with MC-Kun's mom. But, eventually, while MC-Kun and the President were close as kids, the wife wised up and demanded he cut off the other family. And MC-Kun, obviously feeling deeply betrayed, wished to have an ACTUAL little sister-not one that would be torn away, not one that would "abandon him" (I bet she was very cruel when they were separated, but over the years, that turned to guilt...and the guilt into a weird bro-con obsession).
But, as a final act to try and help his son, the father gets him a "special scholarship" to this super rich school, not seeming to realize what a burden that'd actually be
Now, he plays Mahjong to make the money for his mother's "allowances from your father" and does errands for certain people with money for it...like the witch girl.
All while being overseen by the gun-twink and bullied by the rich boy who he cleans out every "Occultism club" meeting.