Why must the total oxidation numbers in a neutral compound add up to zero?

In a neutral compound, the sum of the oxidation numbers must equal zero because oxidation states are a method of conceptually distributing shared electrons among the atoms within a molecule.1

Because this process is a formal calculation rather than a physical reality, the total number of electrons must be accounted for both before and after the assignment. When shared electrons are assigned to the atoms that have a greater attraction for them (based on electronegativity), the resulting oxidation numbers represent the net charges on those atoms. For an electronically neutral substance, these charges must balance out, meaning the sum of the positive and negative oxidation numbers must be zero. For example, in hematite (Fe₂O₃), the +6 total oxidation number of the two iron atoms is perfectly balanced by the −6 total of the three oxygen atoms.12