The part that shows is dead. That's why it doesn't hurt to cut them. But when you get a hangnail, you've accidentally opened up the edge of the living nail root. All proteins are very complicated molecules. They're big and strong, and our bodies use them like building blocks.
Proteins are a part of just about everything in our bodies.
The weird thing about protein is we can't get the parts to make it without plants. Proteins are made out of amino acids, and animals cannot make amino acids for themselves. These ingredients must come from eating a plant or eating another animal that has eaten a plant. The next time you trim your nails, examine the clippings closely. If you have a microscope at school, You Can see the protein fibers.