I used to bite my nails, so I know how hard it is to break. When you have had a bath or done the washing up, push the cuticles back with a towel. This not only exposes a bit more nail so instantly makes them look longer, it also takes away the tension on the bit of skin by the base of the nail that is often red & shiny and has the little sticky-up bits of skin that are so irrestistible to bite. Keep pushing the cuticles back each time you wash your hands; no shiny skin; no sticky up bits; more chance of not biting!
Good luck - it worked for me, now I can scratch labels off things and wear nail varnish!