The mechanism of kidney stone formation is not well understood.“
[…]
Further studies are necessary to fully elucidate the mechanisms of stone formation in patients with nephrolithiasis.”

Source : Minerva Urol Nefrol. 2016

This paper in Biochemical and Biophysical Research Communications Volume 296, Issue 3, explained that :

The process of nephrolithiasis development is poorly understood at the molecular level.“

And this extract from The Lancet Volume 367, Issue 9507, describes how the genetic factors which are assumed to predispose people to kidney stones are also unknown.

Although important advances have been made in understanding nephrolithiasis from single gene defects, the understanding of polygenetic causes of kidney stones is still largely elusive. A substantial proportion of data that resulted in new methods of treatment and prevention, which can be empirical or definitive, has focused on urinary luminal chemical composition of the precipitating solutes. Manipulation of inhibitors and epithelial factors is important and needs further investigation. Advances in the management of nephrolithiasis depend on combined efforts of clinicians and scientists to understand the pathophysiology.”