When a 1φ supply is given to the single winding of the single phase motor, the field produced by it changes in magnitude and direction sinusoidally (pulsating flux).
Such and alternating field is equivalent to two fields of equal magnitude and speed rotating in opposite direction. Such rotating magnetic fields produces two torque’s on the rotor. So the rotor can not rotate in any direction. Because the net torque developed by the motor is equal to zero. So a single-phase motor is not self-starting.