Thyroid disease can cause the nails to become weak and split or peel away from the nail bed, as stated by United States National Institutes of Health's MedlinePlus. Both hyperthyroidism (too much thyroid hormone is produced) and hypothyroidism (not enough thyroid hormone is produced) can cause damage to the nails, skin and hair due to the unhealthy hormone levels.
Other common symptoms of thyroid disease include unexplained weight gain or loss, depression, extreme sensitivity to cold, changes in the menstrual cycle or the development of a goiter, as reported by WebMD.
Aside from thyroid disease, liver disease, nail trauma, kidney disease and vitamin deficiency can all cause the nails to peel. The natural aging process also leads to brittle nails that are more susceptible to splitting and peeling.