If you go a bit overboard and feel a sudden pinch and you start bleeding, It means that something penetrate in your skin and torn off your blood vessel so that you start bleeding.
May be there was any pin or sharp needle thing was there in board that pinch into your skin and your epidermis could not resist that and it is no longer intact and you created a wound on your skin.
Epidermis the surface epithelium of the skin of an animal, overlying the dermis. and in this case it is wounded by that pin.
