in order to use any of its Blue Magic abilities, it must learn its spells from other enemies during battle. Of note, only one character needs to learn a Blue Magic spell in order for the rest of the party to use the same spell.

Source

But why can’t I seem to use white or black magic? Such as Cure, Fire, Ice, etc. etc.

Blue Mages are incapable of using white or black magic. Later, you will get Time Mages who are only able to use time spells and Summoners who are only able to use summon spells as well. The Learn ability is there so you can equip it on a different class in one of your slots so you can learn blue magic spells without having to actually be on your Blue Mage. Any ability that does not have an exclamation mark in front of it does not give you an ability you can select to use, but a passive ability that you use automatically.

If you want to make a Blue Mage who can use black magic, you would need to level someone up high enough on a Black Mage until you unlock the !Black ability of the appropriate level for the magic you wish to use, switch to a Blue Mage and then select the !Black ability as your empty slot skill. For white magic, do the same thing but with a White Mage.

Blue magic can be very strong in the right situations, but I personally am not a fan. It’s too much work to know when you need to learn a skill from something, and too debilitating to to your party to waste a spot on Learn all the time in my opinion (unless you use a guide of course).