Mx0/WMG

Taiga being really weak in comparison to everyone else in the school improved his personality a lot.
We don't really know much about his life before he started to attend Seinagi High we do know a few things which have made me believe that he was Knight Templar Delinquent. It's these two traits that also explain his Love At First Sight with Hiragi. I'll list them first then explain my reasoning. "1st off his physical abilities most importantly his ability to fight and take damage are well above average. 2nd his sister, the only other person we know for certain live in his house, used him as a punching bag for years. 3rd Taiga left, was forced out, of his old school for going on a Roaring Rampage of Revenge against twelve upper class men for picking on one of his classmates. We are lead to believe that he won that fight. 4th He mentions at one point that "Daddy" Hiragi is the only teacher he has ever had that paid any attention to him and was not afraid of him. He never treats any of the other teachers with any respect and does not understand why they would hate him because of that. 5th His decision to break into a school to yell at some girl who laughed at him. 6th When asked what he would do with unlimited power he responded with conquer the world."

Sorry for the reallllly long WMG.
 * We know that he grew up with a sister who is much more physically powerful than him and used him as a punching bag. To the best of our knowledge either his parents didn't care or were unable to stop his sister. So Taiga grew up with someone stronger than him in power and enforced their rule with physical force. This taught him that might makes right, and had the side affect of making him a lot tougher than other children his age. Those two factors gave him a very twisted way of looking a the world and solving his problems. Whenever he came across a disagreement or someone doing something that he did not like he responded the only way he knew how, he fought them. With his superior abilities he got his way which reinforced his assertion that might makes right. So in school most of his classmates are terrified of the hyper violent kid and he does not make any real friends. He does not give teachers any respect at all because they either will not enforce their will with superior fighting ability or they can't do it. They either ignore him or are afraid of him and play by his rules. This explains why I think he is a delinquent.
 * He is a knight templar for a combination of reason. First off his problem resolution is fighting, and second off as much as his sister has shaped his thought patterns he still resents her for the abuse he has to suffer through. So when he sees another someone picking on someone weaker than him he sees red and over reacts in a spectacular way. His inability to hold himself back and his normally violent out look keep even those he saves away out of fear. These two traits are why when he is panicking when asked what he would do with power he responds with conquer the world. It just seems reasonable to him. These two factors also explain why he never really makes any friends in the school. He has allies and his love interest but he does not really trust any of them. He is just not used to having people treat him like a person. Which is also why he adapts so well to being the Fake Ultimate Hero of the school.
 * When he goes to invade Hiragi at the start of the story the reasons that he tells himself are that he wants to get even with that girl, Hiragi although he does not know that yet, that laughed at him. It is heavily implied that he just wanted to see her again because he had a crush on her. Why did he fall in love with a girl who laughed at him once? She is attractive, but she is not drop dead gorgeous and it's not like they had any real interaction. I believe that he got his crush on her because of his isolation up until that point and she laughed at him. He saw it as she was not afraid of him and would be willing to actually interact with him. This is reinforced during the invasion when she is the only one who sides with him and tries to protect him from forces he does not understand in the slightest. Even though in the end she is the one who defeats him which may also have contributed to his crush an inversion of All Amazons Want Hercules.
 * So he starts going to a new school filled with people that have magic, they all have abilities that he cannot emulate no matter how hard he tries. For the first time he is entering into a world of equals as opposed to him being the top dog. This shakes him to the core, for the first time he feels fear about getting into fights which is only compounded be the fact that if they find out that he can lose a fight that he will lose memories of the only girl his age who is not afraid of him and he has a crush on. This has the affect of his living without his central tenant of might makes right for the first time. This start to make changes to his personality.
 * His philosophy is also shaken by the fights that he gets into once he is in the school. He starts to win them not through pure physical skill but through planning and talking to people. The last one is the one that always surprises him, he never believes that people can be reasoned with words before. If you look closely at his interactions with people at the start of series and compare them with how he treats them near the end he is much more open and friendly person. Before Seinagi High he was on the fast track to being in a gang, the Yakuza or prison. With the factors I listed above he has become someone who can actually interact with society as a whole.
 * Very articulate and nicely said. Your view does seem to have good weight behind it. I would also consider the fact he saved Mandrakes, the ultimate weaklings as they are used for potions, more evidence to the idea he can't stand people being beat up unjustly.
 * It could also be said he inherited his view of protecting the weak from abuse from his sister as well. I recall when he faced her double in the second exam, her illness caused her to think she was protecting her brother from harm.