Yea, me and a friend realized that the Spirits actually learn magic in accordance to their element and the mages level, for example
Air Spirit - learns Aero at lvl 9, just like a blm
Earth Spirit - larns Stone at lvl 1, just like a blm.
Ice Spirit - learns paralyze at lvl 4, just like a whm.
note that the spirits learn their spells in accordance to their elemental status, like a lvl 13's earth spirit will learn slow, just like a lvl 13 whm, because slow is an earth based spell. i hope this helps people, if anyone dissagrees, /tell me on diabolos my name is Alyxya and my mule is Zhell