Obsession or Just Experimental? Abnormal or Not?

For more than four years now, our 16-year-old daughter totally refuses to cut or trim down her fingernails. She is extremely focussed on her nails, avoiding quite a lot activities in order not to harm them, or simply gazing at her hands throughout the day.

Any attempt from either her parents or her friends to make her realize that she should cut them back is fiercely being withdrawn. Her main argument is that 'they are me and belong to me'.

What could be the origin of this obsession? Are any similar cases known? Could this behaviour simply be related to puberty or could there be a deeper cause? What would be a way to influence or interrupt this behaviour eventually?