Scholar is a horribly designed job and shows zero thought goes into healer design

[Nizzi]

Without looking it up, here is what I sorta remember about SCH lore:

Arcanists use the "Arcanima", in essence they use geometric patterns, sigils and magic writting to "program" aether into specific forms and functions, essentially a sort of simplified or "degenerated" form of the Ancient's creation magics. Carbuncle is the first construct an Arcanist makes. Bio and Miasma are also constructs, essentially programmed viruses or bacteria that only exist for a very short time, causing damage to the target.

Scholar is the "military " application of the Arcanima arts following the ancient tradition of the Scholars of Nym, a city state that fought against Mhach and ended up succumbing to a Mhachi plague that turned everybody into Tonberry. The scholars of Nyhm were brilliant military strategists that would use their Arcanist magicks to support their troups in battle, stratagems to direct them efficiently against their enemy and weakening magicks to deblitate their foes.

Your fairy is an aetherial construct, just like Carbuncle, born from the SCH soul crystal. A robot made of aether that grows and learns along the scholar. I forgot why it takes the shape of a Fairy or why SCH has a bunch of fairy themed abilities.

Aren't they actual living beings? Lily has a personality, though I could be misinterpreting this.