Causes of hand peeling are multitude and broadly can be classified as:
1. Atopic dermatitis (eczema)
2. Contact dermatitis
3. Infections- Bacteria/ Fungal
4. Immune related disorders
5. Skin peeling syndromes (genetic) e.g Acral
Causes1-2 are most common. As Dr Colin Theng has pointed out, it is advisable to minimise contact with "strong" soap and detergent for e.g by wearing gloves, which can dry out your skin by removing the natural oils. Regular use of hand creams (moisturisers) is also essential. If these measures fail or your condition worsens, please see a doctor.
Hope this helps!
Cheers,
Dr David Deng