What is the driving force behind the half life occurring?
The instability of the atomic structure due to its mass.
How that all works is a bit more complicated, including the probability issues and the wide variety of atomic configurations possible (balance of neutrons, protons and electrons). But basically, the larger an atom gets, the harder it is for the nucleus to hold together in the balance of attractive and repulsive forces.
The “half-life” is an empirical (observed, calculated) formula that describes the decomposition of a radioactive atom into smaller atoms – some of which may still be radioactive themselves. WHY it is the value it is, and whether there is a direct correlation between a mass and a half-life is not known.