If "teacher" cannot be in the objective because of "to be," how can one see [sic] that it is not nominative?

With nouns, there is no change whether they are in the Nominative or Objective. One can know which case they are from the function they fulfil:

She is my teacher : subject complement

He taught our teacher when he was at uni. : object of the sentence

He gave his homework to the teacher. : object of the preposition 'to'.