[pa7x1]

In science why questions are not answered within the framework that raises them, you need a larger encompassing theory that explains the phenomena within a larger scope to answer them. In this larger encompassing theory you can sometimes answer some previous why questions but possibly new why questions are uncovered.

In classical mechanics there is no explanation for the stationary action principle, it just is the procedure you follow to derive the equations of motion (it answers a how, not a why). You need Quantum Mechanics, in particular the path integral formulation of Quantum Mechanics, to answer why classical solutions correspond with action extrema.

Long-story short, in quantum mechanics all possible paths contribute equally to the probability of a particle going from A to B but they interfere with each other. It can be shown that most paths interfere destructively between themselves except when the action gets to a extreme (minima, maxima or saddle point) where constructive interference occurs.

Further reading:

https://en.wikipedia.org/wiki/Path_integral_formulation#Stat...