What physical balance requires exponentially higher core temperatures in massive stars?

Hydrostatic equilibrium

Hydrostatic equilibrium is the essential concept describing the balance within a star: the inward crushing force of its own immense gravity must be perfectly countered by the outward pressure generated by nuclear fusion occurring in the core. For stars significantly more massive than the Sun, the gravitational compression is far greater. To counteract this extreme inward crush and prevent immediate catastrophic collapse, the core must generate correspondingly higher thermal and radiation pressures. This requirement translates directly into requiring exponentially higher core temperatures and pressures, which in turn necessitates a vastly accelerated rate of hydrogen fusion, thereby shortening the star's overall lifespan.