The major reason Mahouka gets on my nerves is it really is a testament to "Informed weakness" in its purest form.
We are TOLD how weak his magic is... so what does he do? He proceeds to magic circles around everyone else.
Is it because he finds some way to make his very little magic work for him? No his magic is just that fantastic.
Basically his magic is more powerful because SCIENCE! which I could accept (after all the amount of Gunpowder in a bullet is nearly harmless) except he doesn't have to work at it or anything. His magic described also isn't getting the most out of a little magic, it is just flat out magic.
The anime is literally trying to make an underdog out of the guy who in a normal anime would be the "Super elite" person at the top looking down on everyone.
Mind you I am REALLY questioning if Mahouka isn't a Parody and everyone is just overlooking that. I mean, it really must be a parody.
The wiki had... sort of some more information on this.
Tatsuya is a child born from the Yotsuba family. Although this is the case, he wasn't accepted as a legitimate member due to the fact that he cannot wield magic. The two types of magic he can freely wield are not considered magic by the family's standards due to its nature of only 'destroying' and 'restoring' information, not 'altering' them.
Which might actually be a fair distinction- oh, he's not a
real mage, because he can't
change anything, he can just blow it up or glue it back together.
In order to allow him to use "magic", his mother and her twin sister operated on Tatsuya when he was 6 years old, installing a magic processor into his mind allowing him to use magic. However, it was inferior to a natural processor so the only advantage the processor granted him was that it allowed him to instantly access short magics (5 steps or fewer) instantly without any buffer or calculation. Since most combat magics use 5 steps or fewer, they are available to him. Also, because the processor can show him the exact magic that needs to be used, he can only use a very long round-about method to execute complex magics (hence why he failed the speed portion of the practical). He is also very adept at manipulating Oscilliation Magic.
Then we have this, which is... trickier. Essentially, he's a savant who can use other types of magic, but only if it's below this certain threshhold... which almost all combat magics are. So again, crippled but not meaningfully, at least in combat.
As a side note, under any other circumstances I'd consider the above a spoiler. I don't think that's possible here.
Of course, then he's also a genius researcher and a martial arts master, and none of the above explains why he's able to, say, defeat gravity. Did he just blow it up or something? Did it take less than five steps? Is he MacGyver even though he has to do everything the long hard way?
Which brings us back to OH NO LOOK AT HOW HIDEOUS HIS BEAUTIFUL ANGEL WINGS ARE SURELY HE WILL BE HATED FOR THEM.