Why doesn’t it hurt when you cut your finger nails?

It doesn’t hurt because there are no sensory nerves in your finger nails. If you hit your fingernail with a hammer, it hurts because the force is transmitted to the underlying finger with its rich supply of sensory nerves. But the fingernail itself is actually not living tissue, and it has no blood supply (which is why you don’t bleed when you cut your fingernails), no nerve supply, no pain.