In introducing atomic orbitals into a qualitative treatment of molecular structure in 1931, Pauling failed to recognise the cognitive dissonance between logical categories of molecules, as physical things, and of orbitals, as algebraic formulae from the solution of the Schroedinger equation for the hydrogen atom in coordinate variables. The failure to disclose systems of coordinates for the hydrogen atom other than spherical polar and the extrapolation of hydrogen functions for application to atoms with multiple electrons enabled Pauling to construct a web of deceit about hybrid atomic orbitals to explain molecular structure in circular arguments. Being precisely algebraic formulae, orbitals have a legitimate role only within mathematical calculations, never in qualitative descriptions of molecular structure.