  We develop a simple yet comprehensive method to distinguish the underlying
drivers of galaxy quenching, using the clustering and galaxy-galaxy lensing of
red and blue galaxies in SDSS. Building on the iHOD framework developed by Zu &
Mandelbaum (2015a), we consider two quenching scenarios: 1) a "halo" quenching
model in which halo mass is the sole driver for turning off star formation in
both centrals and satellites; and 2) a "hybrid" quenching model in which the
quenched fraction of galaxies depends on their stellar mass while the satellite
quenching has an extra dependence on halo mass. The two best-fit models
describe the red galaxy clustering and lensing equally well, but halo quenching
provides significantly better fits to the blue galaxies above $10^{11}
M_\odot/h^2$. The halo quenching model also correctly predicts the average halo
mass of the red and blue centrals, showing excellent agreement with the direct
weak lensing measurements of locally brightest galaxies. Models in which
quenching is not tied to halo mass, including an age-matching model in which
galaxy colour depends on halo age at fixed $M_*$, fail to reproduce the
observed halo mass for massive blue centrals. We find similar critical halo
masses responsible for the quenching of centrals and satellites
(~$1.5\times10^{12} M\odot/h^2$), hinting at a uniform quenching mechanism for
both, e.g., the virial shock-heating of infalling gas. The success of the iHOD
halo quenching model provides strong evidence that the physical mechanism that
quenches star formation in galaxies is tied principally to the masses of their
dark matter halos rather than the properties of their stellar components.
