The word is derived from an agent noun of βαίνω. Indeed, βατήρ exists, meaning "threshold", but this is not the meaning given by the scholion. The idea is that the agent noun has a causative value, so that the staff does not walk, but allows man to walk, makes man walk. That is, the intermediate ghost form *βατηρία is supposed to preserve a meaning which βατήρ does not have. From the formal point of view, the etymology implies the insertion of a consonant, [k]. The fact that agent nouns in -τηρ never form feminines in -τηρία was not considered an obstacle.