You might be wondering about word Muthai. Yes, you are right, name of the river is Mutha, not Muthai. Muthai is combination of two words, Mutha and Aai. Aai means mother in Marathi.
When humans were hunting-gathering stage, they used to gather fruits, dig out tubers and hunt animals. Riverbank proved to an ideal place, due to availability of water, and biodiversity.
When our ancestors began agriculture, they gave up nomadic lifestyle and settled at one place. That is how human settlements happened, grew and civilizations were born.
If you observe, all these ancient civilizations are river civilizations. Our Indus-Saraswati civilization, Egyptian on the banks of Nile and Mesopotamian civilization between Tigris and Euphrates rivers. Rather, word Mesopotamia itself means, between 2 rivers.
Civilizations happened, were nurtured in the cradle of the rivers. That is why, river, very aptly is considered “Mother” in our culture.