Thermal dispersion of the guiding-centre drifts in a plasma leads to phase-mixing and kinetic damping of macroscopic plasma perturbations. A simple illustration is given by the drifts of a low-density gas of charged particles in an inhomogeneous magnetic field. This results in a substantial kinetic damping on a time scale only slightly longer than that of the Larmor period of gyration. The phase-mixing due to the velocity-dependent magnetic gradient drift is also likely to become one of the important kinetic mechanisms in more complicated situations such as those of a dense, non-dissipative, high-beta plasma. In particular, this should apply to the dynamics and stability of macroscopic plasma perturbations in high-beta systems where there are strong magnetic field inhomogeneities.