Why does grey hair grow faster than the regular color hair that surrounds it?

It doesn't.: Gray hair grows no faster or slower than pigmented hair does. However, when the hair turns gray it can often undergo more changes than merely color, such as texture, porosity and wave pattern. These differences may create the illusion of faster growth; but there is no plausible reason that a hair's actual growth rate would be changed by the presence or absence of pigment.