Why do people want Blue Mage in this game?

[Niwashi]

FFV: Blue magic learned (by everyone in the party) when a Blue mage is struck by an enemy ability.
FFVI: Blue magic learned by seeing an enemy ability being used (doesn't have to be the target).
FFVII: Blue magic learned by getting hit by an enemy's skill while having Enemy Skill Materia equipped.
FFVIII: Blue magic learned by using items dropped or mugged from enemies.
FFIX: Blue magic learned by eating weakened enemies.
FFX: Blue magic learned by using lancet on an enemy.
FFXI: Blue magic learned by defeating enemies after they've used a skill.

There's some other differences as well, like under which circumstances that blue magic can then be used, but we've already got a variety of ways of learning it. And the fact that there's already such a variety means that not only could the devs choose from among them the pattern that works best here, but they could come up with an entirely new way of learning the skills and it would still fit in with the rest so long as it's an enemy skill and that enemy is involved in some fashion when learning it.

Personally, I kind of like the IX and X pattern of learning mob skills by using a particular skill on that mob. I think that pattern could work well here. But so could the VI and XI pattern of learning skills you've seen used. The V and VII pattern of needing to be hit by the skill isn't as good of a fit, since hopefully only the tank will be getting hit by a lot of these (or better yet nobody if they're AoE). And the VIII pattern incorporating items into the learning process still just seems a bit strange (though obviously that didn't stop them from using it before, so maybe it could work here too).

Blue Magic is also in VII and works same way as V, everyone can learn it with Enemy Skill Materia.

Ah, right, missed that one (updated above). I left Bravely Default/Second out of this list since they're not officially part of Final Fantasy (despite being so heavily influenced by it that they might as well be.)