In order to become a spellcaster, one must have what is called The Gift. What it is is different between each person who has it, but it amounts to an ability to manipulate and channel magic, whether it be arcane, divine, natural, or something else. Without it, your are more likely to fail, and fail badly, should you try to cast a spell from a scroll without having The Gift.
Note that most magical creatures don't have The Gift. They have a few magical powers. However, the more intelligent the creatures are, and the more magical, it's far more likely that they will have The Gift as well.
It goes without saying that every dragon has The Gift. It just takes longer for it to manifest in some species than others.