Why do planes spin?

Why do planes spin?
There is a obvious reason why planes can glide. Translatory flight is stable... with horizontal stabilizer, the airframe will correct changes of angle of attack.
There is an obvious reason why a helicopter rotor might autorotate. At no translational airspeed, every blade is gliding forward, with leading edge in front and trailing edge behind, just as a wing of a fixed-wing plane. Though I cannot see how the AoA would be stabilized... and it is said that helicopters cannot autorotate directly down, but have to gain translational speed if unpowered.
But why do fixed-wing planes spin? Note that the wings have defined, dissimilar leading and trailing edges. In a spin, one wing is moving leading edge forward, the other is moving trailing edge forward. Why is this a stable state? And why cannot a plane in a spin spiral out and return to a forward glide at a reasonable translational speed and low yaw rate?
There is a obvious reason why planes can glide. Translatory flight is stable... with horizontal stabilizer, the airframe will correct changes of angle of attack.
There is an obvious reason why a helicopter rotor might autorotate. At no translational airspeed, every blade is gliding forward, with leading edge in front and trailing edge behind, just as a wing of a fixed-wing plane. Though I cannot see how the AoA would be stabilized... and it is said that helicopters cannot autorotate directly down, but have to gain translational speed if unpowered.
But why do fixed-wing planes spin? Note that the wings have defined, dissimilar leading and trailing edges. In a spin, one wing is moving leading edge forward, the other is moving trailing edge forward. Why is this a stable state? And why cannot a plane in a spin spiral out and return to a forward glide at a reasonable translational speed and low yaw rate?