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In German, constructions with sein, which is uninflected infinitive meaning "to me", seem to generally use the nominative case. For instance, this is a dog translates to das ist ein Hund, and ein here is in the nominative. In German, this seems related to what the subject of the sentence is.

In any case, I was thinking about this and wondered about why in constructions like it is [inflected pronoun], using the nominative case for the pronoun instead of an objective case seems slightly overly formal.

That's not to say that the nominative case is never used. For instance, from the book of John:

Then Jesus, knowing all that was to happen to him, came forward and asked them, “Whom are you looking for?” They answered, “Jesus of Nazareth.” Jesus replied, “I am he.”

(This is from the New Revised Standard Version, but the King James Version gives the same.) Now, this seems grammatically correct to me, but it probably seem unnatural to the casual listener if, upon asking who Jane Doe is, I answered with "I am she" instead of "I'm her."

Why is this the case? Has this just always been the case in more informal English? Or have there been shifts in usage?