Negative thermal expansion (NTE) in ZrW2O8 was investigated using a flexibility analysis of ab initio phonons. It was shown that no previously proposed mechanism adequately describes the atomic-scale origin of NTE in this material. Instead it was found that the NTE in ZrW2O8 is driven, not by a single mechanism, but by wide bands of phonons that resemble vibrations of near-rigid WO4 units and Zr-O bonds at low frequency, with deformation of O-W-O and O-Zr-O bond angles steadily increasing with increasing NTE-phonon frequency. It is asserted that this phenomenon is likely to provide a more accurate explanation for NTE in many complex systems not yet studied.