+opzero i I felt similar after watching the anime, but in VN it's kind of explained and makes sense. Some theory of magic first: Each person is born with certain amount of something called "magic circuits", which can eb viewed as nervous system of soul. Just like we use nerves to move muscles, magi use magic circuits to move mana. Regular people have really few cicruits(or none at all), while average magus possess around 20. Superb magus like Rin has 30.
Emiya Shirou is random-nobody, regular human so he should have one or two circuits. No magic for this dude, right? Well, yes and no. Although person like that can never bacome a magus, Kiritsugu once stated that every human can use one and only magic on basic level, zero level. It's a magic specific to each human, somethign called "origin" (like Kiritsugu's "origin bullet". It works thanks to parts of his ribs inside bullets). Shirous origin allows him to project image of his mind.
That explains everything, right? No, it doesn't. It's still zero level of projection, it's hardly possible to make anything out of it, not to mention Noble Phantasms. But there is also one thing that allowss Shirou to level-up to ridiculous extent: he doesn't understand a single thing about magic, even if he thinks he does.
With each use of magic magus must activate one or more of his/her magic circuits, which is automatically shut off some time after usage. But Shirou doesn't know that. He thinks a magic circuit has to be CREATED each time he uses magic. So he makes use of his origin magic (projection) and creates a magic circuit each time he wants to use magic. That's why he is such a weakling- he uses one at a time, 20 times less than average magus would use.
However, he does it for five years straight since he bacame Kiritsugu's apprentice (Kiritsugu, you are badass but appearently suck as a teacher). Then Rin Tohsaka comes in and says "Shirou, you idiot! Creating circuits is goddamn dangerous, it's a miracle you didn't kill yourself! You only have to ACTIVATE them!"
So here we are, and even thou those circuits are weak, some of them got destroyed as time passed and only magic he mastered is projection he now possess 27 fully-functioning magic circuits. That's why he is close to being a high-class magi like Tohsakas or El-Melloi and surpasses them when it comes to Projection, his origin.
TL;DR: Because of lack of proper education young Shirou did stupid-dangerous things that made him more powerful than most magi.