Sforno on Genesis 3:20/ספורנו על בראשית ג׳:כ׳

1חוה, she is a necessary requirement for the human species to continue life on earth.

2כי היא היתה אם כל חי, even though the function of the female of the species listed here also applies to all women after Chavah, she is used as the role model and therefore accorded this name. The reason is that she was the first woman ever to fulfill this role.