1. you have a lot of nerves in your fingers, 2. paper is more dull so it does more microscopic damge because it's not just a clean cut, 3. the cuts aren't very deep and most of your nerves are in the top layer of your skin.
Because they are such a fine cut, th good news is they heal and stop hurting pretty fast if you keep them clean And the amount of nerves that are at the end of your fingers, this is why you can feel the different things you touch.
Yes, there are so many nerve endings in that layer of skin that is interrupted by a paper cut. The Good News is that you can wash or alcohol or peroxide the cut, dry it, and use super glue to seal it. It immediately cures the pain!!!