When single phase supply is given to single phase induction motor it produce a pulsating magnetic field, not rotating.
Current through a conductor produces a flux. This flux can be resolved into 2 components, each one rotating in the opposite directions at the same speed(slip).
As a result, the net flux is zero, the induced current in the rotor conductors is zero, resulting in zero torque. So, a single phase induction motor is not self-starting.
Single phase induction motor has distributed stator winding and a squirrel-cage rotor. When fed from a single-phase supply, its stator winding produces a flux ( or field ) which is only alternating i.e. one which alternates along one space axis only. It is not a synchronously revolving ( or rotating ) flux as in the case of a two or a three phase stator winding fed from a 2 of 3 phase supply. Now, an alternating or pulsating flux acting on a stationary squirrel-cage rotor cannot produce rotation (only a revolving flux can produce rotation ). That is why a single phase motor is not self-starting.