Question

why do electric motors burn out if they are switched on but no allowed to rotate?

Answer 1

When electric motor is turned on, it acts as a generator and produces a back EMF that opposes the applied EMF. Ideally,   A frictionless motor would draw no current when not under load, though obviously real motors do draw some current because of frictional losses.

If you load the motor you reduce the back EMF, and because the applied EMF is now greater than the back EMF there is an increased current through the motor.

If you stall the motor completely then it does not generate any back EMF at all, so the applied EMF sends the maximum possible current through the motor, limited only by the resistance of the coil windings. Depending on the motor design this may be high enough to damage the motor.