Made a stupid error

[Mikazuki_Aura]

The error you speak of will only occur if you attempt to equip a class without a matching class weapon in your Armoury Chest.

If you equip a set even though armour/accessories have been shifted off, it will give you a notification, and then equip all items except the now-unavailable items.
If you equip a set even though its weapon is no longer available, it will give you a notification, and then equip another weapon in the Armoury Chest that class can use.
It will only fail if no such weapon is available in the Armoury Chest, as the game uses your weapon to decide your class, and thus wielding no weapon at all will not allow the class switch.

Having weapons in your inventory will Not Work. It must be in the Armoury Chest for the game to use auto-equip on it.

You've already solved your problem manually, but keep this in mind for future reference. It is not necessary to reform a set from zero.

Also for future reference: Equipment pieces that are currently registered in any Gear Set will always have a small note-like icon next to them. Do NOT move any of these pieces to a retainer, convert them to materia or disassemble them. Even if you want to change a piece through all classes, change all of the gear sets first and then remove the piece after it has been first replaced in all sets, or else you risk accidentally entering battle with a piece of equipment missing.