How do I use the Blue Mage in Final Fantasy V?

I’m playing Final Fantasy V on an emulator, so I thought at first it was some kind of glitch, but I guess I just don’t understand. I’m very early still in the game, about to enter the North Mountain. But I’m confused as to why my Blue Mage can’t use the spells I bought in town, such as Cure, Antidote, Fire, etc. I read up and know now that the Blue Mage can extract spells from certain monsters, but does that mean he/she can’t use White or Black Magic? That sucks then. . .The Learning ability confuses me, because I equip it but it doesn’t show up on the menu. Does it only appear if I run into an enemy I can learn magic from?