Well, standard statutory construction; the only thing in the rules that affect specific eidolon base forms are certain evolutions. Nowhere does it say that a spell can affect only a specific base form. He is trying to create rules. There is no way you can disprove him, because his rule doesn't exist.
Much like (to the best of my knowledge) nowhere does it say that you need teeth to cast spells, even though it is very difficult to form the correct sounds without teeth.
Sadly, the DM never has the burden of proof; DMs control the world.
But the reading of the exact language is quite clear. "Share Spells (Ex): ... A summoner may cast spells on his eidolon even if the spells normally do not affect creatures of the eidolon's type (outsider). ..."
Enlarge person affects humanoid. This is not "Earthbound Humanoid". And I do not think there is such a thing as an "Outsider Humanoid" (but I could be wrong). Your DM is making up distinctions.