Kevlar is a fabric consisting of very strong fibers. Ever poked through your shirt with a pencil? Ever tried it with the eraser? Rifle bullet is pencil tip, pistol bullet is eraser, shirt is kevlar. Rifle bullet has to break less fibers before it can start pushing them aside instead, which is easier. They also tend to be travelling a lot faster.
Metals are mostly homogenous on the scale of a bullet. Rifle bullets still do a better job of penetrating them due to speed/shape difference above, but they resist deformation in every direction whereas fabrics resist deformation only in line with their fibers. This is an example of isotropy vs anisotropy.
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