I vaguely recall they seemed to hypothise he must've had a tiny bit of elven blood in his veins, and then just handwaved it with that.
That's what I assumed before I met Zelos, in any case. It must've come from somewhere.
Where did Kratos' magic come from? I don't think transforming into an angel gives you elemental spells per se, just Light and Dark. I always assumed Kratos has the same stuff in his blood as Zelos.
Apparently Sheena tells the party Zelos had elven blood transfused as an infant, in order to use magic. I seem to recall Zelos tells the party it was Aionis Ore though.
edit: Apparently Zelos got Aionis from Cruxis and told the party he was injected with Elven Blood as a cover up story.
Altessa of all dwarves seemingly confirms Kratos has Aionis in his blood as well.