I am working from my memories of physics here. I probably know only enough to be dangerous, but here goes:
Stabilization is a tug-of-war between those external forces acting on your bullet and the inertia created by rotation. If the inertia is greater than or equal to those external forces, the bullet is stable, if not, it will precess, yaw or tumble.
The inertia (resistance to acceleration) is created by a phenomenon known as
angular momentum, which is created by the spinning of the bullet in the rifling.
The external forces are largely the result of resistance of flying through the medium. A bullet does not "want" to fly point forward, because the higher surace area/ mass ratio of the nose creates more drag that encourages the nose to trail the base ( the bullet wants to fly backwards). The denser the medium, the greater the forces of drag, and the greater tendency to flip the bullets around. This is why bullets can be stable in air, but yaw in flesh.
Another big event in a bullet's life is exiting the the bore. In the barrel, the bullet is forced to spin about its geometric axis, which is the physical centre between the bearing surfaces. In air, though, it must spin about its centre of mass. If a bullet is not concentric, it will shift its centre of rotation in the first few metres after leaving the bore. A large shift at this point may induce wobbling from which the bullet will never recover, leading it to precess or yaw in flight.
That then gives us three things that may cause destabilization in flight:
- medium being travelled is too dense
- medium is not of consistent density. A network of twigs in a matrix of air would be an example of an inconsistent medium
- A poorly formed bullet that has a geometric centre that differs considerably from the mass centre.