The cause of the break-up of the aircraft in the JFK Jr accident and the wings coming off as a result of pulling up too abruptly from a high speed dive are the same... excessive load factor (load factor = Lift / Weight and is measured in g forces).
Load factor, in these examples, is created by up elevator increasing the amount of lift produced by the wings. All components of the airframe have a limit to the amount of force (weight or load) that can be applied before they break. Above a certain airspeed the wings can generate enough lift that the resulting load factor exceeds the airframe strength.
A very common point of breakage is where the wing attaches to the fuselage, or where the horizontal stab attaches to it, but depending on how the aircraft is loaded (how close it is to its maximum weight) it is possible to have some other component fail before the wings even get close to failure. The engine mounts for instance.
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This created a conflict of forces acting on the aircraft, creating a tighter circle to spin in and to make a long story short, his wings broke.
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There is no conflict of forces, merely too great of a load factor for the airframe to withstand.
The conflict (in the case of an accident like JFK Jrs) is with the pilot's senses, and the pilot relying on his senses rather than his flight instruments.
One must use all the flight instruments, not just one or two, to make sense of what is going on. Flight training is supposed to cause your reactions to be different than instinct, and instrument training teaches you to properly read and interpret the flight instruments and base your reactions off that interpretation so that you don't wind up in JFK Jrs predicament. JFK Jr was not instrument rated, if he had been he'd probably be alive today.