Question
Why are menstruating women (at least in the Brahmin community) asked to be separate from the family for three days?
Answer
Menstruation is considered to be "muci," or impure. For many brahminical families, temple worship and puja were their primary occupations. One cannot worship the Deity or perform rituals if one is unclean. The concern was that women would contaminate the offerings prepared.
Manu-smriti / Discourse V - Sources of Evil / Section IX - Other forms of Impurity
(Sanskrit text, Unicode transliteration and English translation by Ganganath Jha)
रात्रिभिर्मासतुल्याभिर्गर्भस्रावे विशुध्यति ।
रजस्युपरते साध्वी स्नानेन स्त्री रजस्वला ॥ ६५ ॥rātribhirmāsatulyābhirgarbhasrāve viśudhyati |
rajasyuparate sādhvī snānena strī rajasvalā || 65 ||In the case of miscarriage, the woman becomes pure in so many days as there have been months; and the woman in her courses becomes fit by bathing after the ceasing of the menstrual flow. — (65)
दिवाकीर्तिमुदक्यां च पतितं सूतिकां तथा ।
शवं तत्स्पृष्टिनं चैव स्पृष्ट्वा स्नानेन शुध्यति ॥ ८४ ॥divākīrtimudakyāṃ ca patitaṃ sūtikāṃ tathā |
śavaṃ tatspṛṣṭinaṃ caiva spṛṣṭvā snānena śudhyati || 84 ||After having touched the Cāndāla, the menstruating woman, the outcast, the woman in child-bed, the dead body, or toucher thereof — one becomes pure by bathing. — (84).
On a different note, women were allowed to fully rest during menstruation and were excused from all household duties. This led to quicker recoveries and happier women.
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