Brutally honest? It reeks of anime tropes.
First and foremost, the movers and shakers of the world will almost never have introverted children, you're more typically going to be ambiverts with at worst a tendency to introversion, due to social standards among their class as well as familial expectations in addition to the interactions among their peers of their social rank. Its no doubt going to be something taught at a very young age, with certain charismatic tendencies picked up through the child's mind modeling itself after how their parents think and act in public based upon what they also are told is right in society. Not saying they're happy go lucky, party hard 24/7, but they will have a tendency to not be shut ins with no ability to control their emotions.
Second, the inclusion of magic is almost entirely arbitrary. If magic exists in the world, which you explain it does, with it being a known and studied art and science, eugenics would be incredibly popular. Like insanely popular. Showing the SLIGHTEST inclination would immediately put yourself above your peers and in a class well above anybody else. You'd also be the subject of reverence and testing. Betterment of the human race and all that.
Third, people who tend to think this way you've described are also incredibly strong willed. They're the ones who also tend to blame things on themselves. It could make an interesting conflict of character but you'd need to have some sort of involvement of the MC's friend' death to make this somewhat believable for his character, that being an introvert. To jump off of this, if you're going to go full military, there is ramifications to this as well. If it's modern day, the military where magic exists is only going to be that much more grueling, holding to of higher standards, strict and breaking as well as rebuilding. If you're going to go in for Magic Combat wingding, you're going to have to first meet standards and if you meet those, you're going to be trained to be better, whether you like it or not. In addition to this, the sister thing is silly. Unless its contained to the family and social circle, no one in the military is going to know nor care because Kill Hats do not act impartial to anybody, you're all trained in the shit, because you're are shit and you will come to enjoy the shit, together as a team because while you may be right when saying "I am shit" you forget everybody is also saying the same thing.
Fourth, while I have no problems with psychological issues becoming apparent from stress breaking down a person's mental stability, its something that happens over time with the little bits and pieces eating away for the certain major blows to hit the heart, before the mind tries to repair itself.
Fifth, you need serious build up to this. Society would need to be seriously screwed up if joining the military was considered a great dishonor and hospitalizing your own damn son was something ignored by authorities especially if it was an act of violence inflicted on a military personnel. Double for your MC actually fighting in something outside of self defense. At best, he'd be dishonorably discharged. At worst, facing time in prison.
Sixth, while people do display light sociopathic tendencies, its not a full blown flick of a switch. You seem to build up to this but its not just becoming logical, people are logical even when they seem like they're not. In fact, sociopathic tendencies inflict the opposite, and what you end up seeing is people who will live normal lives but during periods of psychological or emotional stress simply ignoring or disregarding the issue while taking a passive aggressive stance to it, most commonly in the form of simply not caring.
Seventh, you've created a conflict of setting. If there was a conflict great enough to from the looks of it, permanently scar the MC because of his father's actions, I think the last thing they're going to do is interact with him, nor would them interacting with him be a cause of distress simply because he wouldn't care seeing as it is illogical, even if it was an accident.
So while it is interesting that you're trying to subvert the "Anything is possible if you put your mind to it" idealistic retarded fantasy about life that is so common in media and real life as well, you subvert it to the point where your character seems more childish, brooding edgy ninja highschool that deviates from reality when it serves to further the plot.