It is sometimes said that if you pluck a white hair, several will grow back in its place, but this is not the case. Indeed, hair pigmentation is determined by the proportions of eumelanin, a dark pigment, and pheomelanin, a lighter pigment, in the hair fibers. These are two types of melanin synthesized by melanocytes.
Pulling out a white hair does not affect the ability of melanocytes to produce melanin in other follicles. Moreover, hair grows according to an independent growth cycle for each follicle, with phases of growth (anagen phase), rest (catagen phase), and shedding (telogen phase). When a hair is plucked, the cycle of other hair follicles is not disrupted.
However, it is still advised against plucking out your first gray hairs. Besides being only a temporary solution to hair whitening, this action is harsh on the scalp and goes against the hair renewal cycle. To defend itself and fill the void left by the hair in the hair follicle, the scalp reacts by stimulating the activity of the sebaceous glands, which are responsible for sebum production. As a result, hair may appear greasier. It is also possible that some people experience scalp itching after plucking a large number of hairs.