My daughter did the same thing.
It took me taking her through some mature education...OK, and bribing her with nail polish, but the education carried more weight.
I started with a little education about colds and flus, and the importance of handwashing in prevention. Then I taught her a bit about the skin layers....how your body is water proof, and it protects you from so much..especially germs. But when you put your hands near your eyes nose and mouth, you can catch germs. I made sure to stress that when you don't wash your hands, germs enter the body when your hands get close to your eyes, nose and mouth...those are openings. Especially washing hands before you eat prevents you from bringing the germs from your hands into your body on your food. I even went as far as explaining that sometimes picking your nose is giving you more germs than your "picking out". I also told her about forensics (I worked in medicine) and how cultures under the nails are germ colonies. Not only germs you pick up from touching door knobs, but the germs under the nails don't 100% wash away when you wash your hands.....so they have time to grow, colonize. When I scrubbed at work, we had to use nail picks and scrub under hte nails..Its a whole village of germs under there and she was putting it in her mouth when she was biting the nails. Finger nails have no business in her mouth. NOw to add insult to injury...she is biting the cuticle...leaving openings in the skin right on the hands....Hand washing is not enough, she has to keep them covered since she broke the skin. Everytime she whined about having a cold, sniffles or a cough....I'd ask to see her fingers. I'd blame her hand washing/hygeine or nail biting. Infection is not just green gooey stuff in the cut...it is germs, colds, flus and deadly diseases too.
Ok, then we saw a great show on I think The Discovery Health Channel (my daughter loves the gross medical shows)...it was about a woman who caught a Staph virus when her daughter sneezed on an open wound on her hand. It opened up a whole conversation about the dangers of open wounds in vulnerable areas like the hands. Well...in the TV show, the virus attacked her damaged shoulder tissue, not the local area where she was initially infected. She ended up with a necrotizing infection and lost most of the muscle of her arm...the staph just decayed it. SHe had to have multiple surgeries to remove the dead infected muscle tissue. The germs picked out the weakest tissue in the body and she had a recent shoulder injury that was healing. It was an eye opener for her to see a nasty internal infection being traced to a break in the skin from a hang nail.
Now, working in medicine, I admit that I do get a bit germaphobic. I see people with hepatitis and HIV walking around like everyone else. I saw someone with HIV AND Hep B walking around with a burn on his hand, and it wasn't covered. Maybe it wasn't intentional, maybe he just had no clue he is spreading his disease to the public. Maybe he was not mentally capable of understanding his illness...but he was in fact touching everything putting everyone else at risk. It made me cringe thinking about every hand rail, door handle he has infected in the public. OK, HIV dies once its dry....but Hepatitis lives in a drop of blood for days. Touching things with open wounds is like licking a public toilet seat. So I am very obsessive about hand washing in public and protecting openings in the skin from infection.
I tell her often how inappropriate it is to have open wounds on the hands. People will think she is spreading germs too....and worse, she is exposing herself. In some countries, you do not go in public with a cold unless you wear a mask. You don't lick public doorknobs...its gross....you don't touch things with open wounds....
SO if she bites her cuticles to a point of open wounds, she has to cover the wounds. Hands are too public...they touch everything.
Buy a couple boxes of bandaids...use them everytime you see a break in the skin....
Maybe he will catch on how important the skins integrity really is.
Educate him.
It's not just your pet peave, it is important.