We know,
-Magic is teachable, someone just has to teach you the spell
-You can cast very fast (implying that no verbal commands are used)
-spells can be manipulated in different ways (jet-of-fire, fireball, etc)
This is my idea.
It might be farfetched, but is anything about magic have to be realistic?
Magic has certain energy signature, like fingerprints. Once you learn this magical signature from the vast sea of dismembered hands that is magic, it becomes easier to bring it out. The more powerful the spell, the more deep and complex the signature is. Experience with magical fingerprints of a likeness, makes you better at that group of magic.
This is just an idea, might be stupid, but I can't think of anything else.
I know the magic system is mostly due to gameplay, but does it hurt to flesh it out a bit?