The decomposition of hydrogen peroxide is said to have the following two. 
1. H2O2 → H+ + HOO- 
2. 2H2O2 → 2H2O + O2 

The combination of alkali is essential to promote decomposition. 
It is the decomposition reaction of 1 that works effectively for bleaching, and the presence of metals such as iron and copper or their ions accelerates the decomposition reaction of 2. 
The decomposition reaction of 2 causes oxidative degradation of cotton, which leads to strength reduction and pinholes. 

Stabilizer for hydrogen peroxide bleaching achieves uniform bleaching by suppressing rapid decomposition of hydrogen peroxide.
It prevents degradation of strength and pinholes by suppressing decomposition of 2, and plays an important role to obtain high quality bleached products.