(another way)

Let me say it another way. Here is our sentence.

The direct object answers the question of "What?" What does Peter hear? Peter hears the "teacher." The action of the very is done to the direct object. to;n didavskalon is therefore accusative.

But when you use eijmiv, it draws an equals sign. "Peter is the teacher." "The teacher is Peter." And so "teacher" can't be the direct object because it does not receive the action of the verb. Therefore, "teacher" is not in the accusative but is in the nominative, just like oJ PevtroV.