means Drying up and shrinking from lack of vitality, or — of a look or remark — so cutting it seems to make the target shrivel.

from From Middle English 'wydderen,' a variant of 'wederen,' meaning to expose to the weather — the same root as 'weather' itself. A withered plant is, quite literally, one the elements have worn down. The figurative use — a withering glance, a withering remark — leans on that image of something left to dry out and curl, now applied to pride instead of petals.