How does magica work ?

[myahele]

In regards to ACN:

“Adepts of the art of arcanum derive their might from symbols of power born of geometric techniques hailing from across the southern seas. Held within occult grimoires, these symbols lend shape to the arcanist's aether, thereby allowing him to produce myriad powerful spells.
Using the selfsame symbols to unlock the latent power contained within gemstones, arcanists are also able to summon forth the familiar known as Carbuncle to carry out their bidding.”

In other words they use aether around them and funnel that aether into their books. That book has an "algorithm" that then shapes/programs it into a carbuncle. Additionally, gemstones contain "power" which explains why carbuncles are all named after the gemstones used in their creation. Additionally, THM/BLM use gemstones in their weapons to channel aether.

When they're finished with Carbuncle that aether is dissipated back into the land

SCH and SMN operate under the same principal due to their base as an ACN, but there are differences on the top of my head:

SCH:
Unlike Carbuncles; Faeries are permanent and are bound into their respective soul crystal. Think of them as a more advanced carbuncle especially since they'll retain all the knowledge of their previous scholar to wield them

SMN:
You summon forth the egi/essence of the primal and beat it into submission.

In either case, the amount of aether capacity/reserve you have is important. You need to have at least enough just to be able to cast spells as seen with one of the THM brothers who wanted to become a THM like the rest, but lack the aether capacity to even cast a fire spell.

Due to that, it seems like there are people that simply cant become mages