The likely culprit is that you're using magic as a secondary ability and the character doesn't have access to the right skill level for it. For example, and I am pulling these numbers out of thin air, Bartz is likely at Lv. 4 in the Black Mage job, whereas Galuf only has a Lv. 1 or 2. This means Bartz can use Lv. 4 Black Magic while Galuf can only use Lv. 1. Your magic access is directly tied to their job levels because the magic upgrade you get allows your character larger access to the class's spell repertoire and also boosts their effectiveness.

So long story short, you likly need to change Galuf back to a Black Mage and grind a few additional job levels to gain access to the appropriate spells. Likewise, Red Mage class gives you access to both White and Black magic, but even at it's highest ability level, you only gain access to a third of the magic spells available to both classes.