Step 1: Define the relationship in the given pair precisely: DOCTOR is a professional, and HOSPITAL is the type of institution where that professional is formally based and employed, not merely a room or a person they interact with.
Step 2: Apply this exact relationship to TEACHER. Ask which option names the institution where a teacher is formally employed, as opposed to a person the teacher interacts with or an object the teacher uses.
Step 3: Eliminate mismatched types: 'student' is a person the teacher interacts with, similar to a patient for a doctor, not the workplace. 'Book' is a tool, similar to a stethoscope for a doctor, not the workplace. 'Classroom' is only a single room inside the larger institution, similar to calling a doctor's workplace an 'operation theatre' instead of a hospital, too narrow.
Step 4: 'School' is the full institution that employs teachers, exactly parallel to how a hospital is the institution that employs doctors.
Correct option: (2) School.