Basically, girls stay at home because they lack sanitary protection and towels; they stay at home to avoid staining themselves with blood and getting embarrassed in school and in public.
Many traditional patterns of behaviour, especially seclusion and reduced mobility for women, derived from earlier lack of suitable sanitary protection, and continued long after more adequate materials were available.
In promoting education for women as the most effective way to both raise their status and limit disastrous population growth, availability of convenient sanitary protection is a must.