
Dragoon and White Mage are the Jobs with the most trouble for roleplaying if you want to stick to the lore. As Naunet said, I think that if the game mechanics allow you to be a certain class, then you free to be it on your characters. This is a clear case of the developers trying to bake the cake ("White Magic/Dragooning is, like, super speshiul!") and then eat it ("You, our players, are super speshiul!").
But there's been enough of that.
For all the other classes, Sounsyy has covered them. I will chime in to talk about Summoners and Schoalrs, though: EDIT: Or FreeLanceWizard will come in, do it before I do and better.
SMN: The canonical storyline has a Miqo'te woman actively tell you about summoning and teach you about it. The only stated requeriment for summoning is that you have to be 'dowsed' in a Primal's essence, in this case by defeating them. Mechanicall, your summons are locked until you complete the corresponding Primal fight. This tells us summoning can and is being teached to Arcanists as long as they were present in a fight against a Primal, a thing which, in itself, is also inside the realm of possibility as Primals are constantly summoned by the beast tribes.
SCH: You become a Scholar by finding a fairy (and the soul crystal) locked inside a Nymian chest (or something like that). The questline is pretty much all about running around trying to unlock your fairy's memories and being taught about Nymian tactics by an erudite marauder. It is quite safe to assume that one could study the spells and learn to use them even without a fairy.
The only thing to keep in mind is that all Jobs require a Soul Crystal. We know they exist canonically as you are not only given one in the storylines, but they feature prominently in some of them (like Warrior's). How you acquire one is up to you.
But there's been enough of that.
For all the other classes, Sounsyy has covered them. I will chime in to talk about Summoners and Schoalrs, though: EDIT: Or FreeLanceWizard will come in, do it before I do and better.
SMN: The canonical storyline has a Miqo'te woman actively tell you about summoning and teach you about it. The only stated requeriment for summoning is that you have to be 'dowsed' in a Primal's essence, in this case by defeating them. Mechanicall, your summons are locked until you complete the corresponding Primal fight. This tells us summoning can and is being teached to Arcanists as long as they were present in a fight against a Primal, a thing which, in itself, is also inside the realm of possibility as Primals are constantly summoned by the beast tribes.
SCH: You become a Scholar by finding a fairy (and the soul crystal) locked inside a Nymian chest (or something like that). The questline is pretty much all about running around trying to unlock your fairy's memories and being taught about Nymian tactics by an erudite marauder. It is quite safe to assume that one could study the spells and learn to use them even without a fairy.
The only thing to keep in mind is that all Jobs require a Soul Crystal. We know they exist canonically as you are not only given one in the storylines, but they feature prominently in some of them (like Warrior's). How you acquire one is up to you.