Why don't single-phase induction motors self-start?

Single-phase supply produces a pulsating (not rotating) magnetic field, which can be resolved into two counter-rotating fields. At standstill, these produce equal and opposite torques, resulting in zero net starting torque. Once running, one component dominates due to different slips. Starting methods create phase difference between windings: capacitor-start, capacitor-run, split-phase (resistance), or shaded pole. These produce a starting rotating field sufficient to develop starting torque.