Here's why:

• "On" is generally used for surfaces or specific locations ("on the table", "on Monday"). In this context, it's not suitable as the teacher isn't necessarily on the surface of the school building.
• "Onto" implies movement onto a surface or position ("He jumped onto the stage"). While the teacher might be moving, the sentence doesn't explicitly mention the direction or intention of the movement.
• "In" is often used to indicate being within a place or enclosed area ("The teacher is in the classroom"). This is the most appropriate option as it signifies the teacher's presence within the boundaries of the school.
• "Into" implies movement entering a place ("He walked into the room"). Similar to "onto", the sentence doesn't explicitly mention the direction or specific movement towards the inside of the school.