As a main character, Shiba Tatsuya is boring to hell. He does not emote, or show any emotion whatsoever. There's an explanation as to why he does this, but you don't find out until the end, hell I'm not even sure that I figured out in the anime, I think i had to read the manga to get the full explanation.
His abilities also rob the series of any conflict or challenge whatsoever because within the middle of the anime, I figured out that basically he'll pull some technobabble out of his pants and own the competition no matter how hard they tried. I hate to spoil, but the thing is... Tatsuya's disability isn't actually a disability. It's one of those blatantly stupid "he's too powerful to do simple stuff, he has to use nuke powers and nothing else".
Combined with Tatsuya's bland character, the abilities he has writes out any meaningful conflict within the series. The series tries to say he struggles to do what he does, but he doesn't emote, so he never shows it.
This is not to say non-emotional characters are boring, but they need to be written better so that their lack of an emotion is an interesting conflict. Unfortunately, the Irregular at Magic High School has people throwing themselves in praise of Tatsuya despite the fact that... he's got the emotions of a robot, and is a bit of an arrogant jerk to boot.
The problems with Tatsuya as the main character extend to the rest of the cast, who embody basic anime cliches to the point that I sometimes find it difficult to differentiate the male members of the cast from one another as they often embody the same "comrade/buddy" cliche. His sister's characterization is even worse as she's portrayed as an emotional woobie, but a magical powerhouse... which would be interesting if she actually faced any kind of meaningful conflict her brother wouldn't just solve in two seconds.
These poorly written characters thus really don't do well for the story, which can't give a conflict that Tatsuya and his band of overpowered, bland, ensemble cast members can't solve without too much difficulty. Thus the story... suffers.
To make matters worse, while the art is pretty good, the actions scenes... are not well-designed. The magic system they use is a technobabble system that relies on strategy/cunning rather than simple brute force. But... it's so technobabble heavy nobody can understand whats happening and so it instead becomes an excuse for Tatsuya to make stuff up and own everybody. And yet, one can't get a good sense of how crazy this is because the system itself isn't really flashy, so no tension or sense of fulfilment is built up.
At their worst, fight scenes thus devolve into, who can spew more technobabble. At their best, they're...people hitting each other with special swords or shooting each other with guns. Not particularly fun for a Shounen anime.
