All skills come form job quests that send you out to fight 1 or 2 mobs and acquire their skills by either seeing them or getting hit by them depending on the mob.

Blue Mage could have some party damage mitigating effects such as Mighty Guard to mitigate a very small amount of damage for big attacks or tank busters, and small party heals to help Healers in time of need such as White Wind. Abilities that cause status effects also deal some damage to not make them "completely" useless on monsters that are immune to the status effect.

This is how I thought Blue Mage would work. You would go back to your Trainer, they tell you to go fight a Cactuar some where in the open world. You fight the cactuar, get hit or see 1000 needles. Learn the spell when you kill the mob, go back to the Trainer. They say "good job, I'll let you know if I think of any more monsters you can learn from," or "come back when you're stronger and I'll tell you of a new mob to try to learn from."