(Hebrew חוה) Havah (Eve) means "life giver." It is written with the letters Chet, Vav, Hei and is pronounced “Havah,” and is derived from the word “chai” which means life. Eve is a symbol related to the sexual organs, whereas Adam is related to the brain.
Genesis 3:20: And Adam called his wife's name Eve (Chavah); because she was the mother of all life (Chai).
After the division of sexes, the brain (Adam) in the masculine body kept the development of the seed (zoosperm) in the testicles whereas the brain (Adam) in the feminine body kept the development of the egg (ovum) in the ovaries. Both organs of procreation are EVE, however, the sexual organs of the feminine body are responsible for the entire process of development of the human embryo, this is why the female and not the male body receives the title of Eve (mother or life giver).