Trying to get Arcanist job

[Enkidoh]

More to the point, ACN is a class not a Job. Also unlocking classes is not connected to the main scenario, it just requires you to get to level 10 in your starting class and complete all the class quests given by your starting class's Guild up to and including the level 10 one - you'll know you have passed this point if when you completed that quest the Guildmaster for your starting class tells you that you have been granted leave to try your hand at other Disciplines, and completing the level 10 quest will outright tell you in big letters 'ARMOURY SYSTEM UNLOCKED'.

This may sound odd but, have you already unlocked it? The reason is believe it or not many people have done that in the past, unlocked a class then never touched and it and completely forgotten they did so, then decide to go back and think they still need to unlock it despite having already done so (and wonder why the quest is not available). To check, you can either open the Journal and under 'Completed Quests' check class quests and for ACN class quests if it lists the starting class, or open the Character menu and click on the Classes and Jobs tab, and for Magic DPS, if ACN has a zero next to a slash and a set of numbers to next level, you have already unlocked it. If it just has dashes then you haven't unlocked it yet.

A third way of checking to see if you have already unlocked it or not is probably the simplest way - just get a level 1 ACN grimoire and try and equip it. If it doesn't let you then you have not unlocked it (either you haven't unlocked the Armoury System itself which allows you to change class, or you haven't unlocked that class).