These motors are usually squirrel cage induction motors. That means the rotor is excited by transformer action from the stator, and consists of a few shorted windings on a transformer-iron (soft iron) core. It has nominally no magnetism of its own, though the soft iron may have a little residual field from its last use.
If you spin it, there is little magnetic field in the rotor, so little voltage generated at the terminals.
You can use an induction machine to generate power, but it must be connected up to the voltage source first. When you connect it up, it will run as a motor, with a small amount of slip. If you apply a load, the slip will increase, and it will draw power from the supply to feed into the load, as you'd expect from a motor.
If instead of slowing it down with a load, you speed it up mechanically, the slip will decrease, and go negative when its speed exceeds synchronous speed. Under this condition, it will take mechanical power from what's driving it, and push power into the electrical connection.