They probably wanted her to be safe, till she was grown up enough to look after herself and venture out into the world. Eiko and Garnet both have a few Eidolons already, but for Eiko to gain her 'own' special Eidolon, that'd mean losing her life-long companion, Mog, who was created for the sole purpose of protecting Eiko by transforming into Madeen when the time was right.

It's just so that Eiko won't be all alone while she's growing up, I think.