Why rivers are considered sacred: Indian civilisation grew on river banks — Harappa on the Indus, the Vedic settlements on the Saraswati, Varanasi and Patna on the Ganga. A river gave drinking water, irrigated fields, carried boats and never asked anything in return. What gives life without asking is treated as divine, so rivers became objects of worship, with festivals such as Ganga Dussehra, Chhath and Pushkaram held on their banks.
Why most are female: A river feeds, cleans, carries and forgives — the qualities Indian tradition associates with a mother. So rivers are addressed as maa: Ganga Maiya, Yamuna, Godavari, Kaveri, Narmada. Grammar helps too — most river names in Sanskrit are feminine nouns, and the goddesses of the Ganga and Yamuna appear as women in temple sculpture.
The male exceptions: The Brahmaputra ('son of Brahma') and the Sone are masculine in name and in nature — huge, fast and famously destructive in flood. So is the Damodar, once called the “sorrow of Bengal”.