Explanation:

Nails are usually made up of thick and multiple layers of a type of protein known as Keratin and are composed of dead tissues. They are devoid of any nerves and blood vessels and therefore we do not feel any pain while the nails are being cut.

Nerves act as messengers to convey the sensation of pain and in their absence it cannot be perceived by our brain. You will feel pain when the nails are pulled as the nail bed (below the cuticle) is replete with nerve endings and blood vessels.