Through exhaustive studies, the witch Starlight Cosmos has postulated convincingly that ALL people are capable of magic, but must both learn it and believe in their own ability to use it, with increasing effectiviness the lower the age they begin.
The trick here is of course that magica is dangerous, especially in the hands of children and young people.
It has long been considered prudent to delay any teaching of magic until the student was past their 16th year, but this in turn has led to a shortage of magic users.
Of course adults can, and do, learn magic BUT mentally they often struggle to truly comprehend and believe in their own abilites.
Foundations for safely teaching children Magica manipulation are now being set up, and we may be at the beginning of a new age of much wider magical usage.
-On Magica and Wizardry, 12th edition