A school always has
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Principal
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Teacher
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Building
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Library
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Classes
A school must have teachers to function as an educational institution. A building, library, principal, or classes are common features but not strictly necessary - teaching can happen in various settings without these elements. The essential element is the teacher who provides instruction.
This tests which attribute is essential to the definition of 'school' versus incidental. A school, by definition, requires a teacher to conduct instruction -- that's the defining function. It need not have a distinct 'principal' title, a dedicated 'library', a formal 'building' (some schools operate in temporary or informal spaces), or scheduled 'classes' in the rigid sense implied. Teacher is the one element that's conceptually indispensable to what makes something a school.