God created Eve to
(1) make Adam complete, since without Eve (the flesh of his flesh, bone of his bones), Adam is incomplete;
(2) be Adam's companion and helper, since without Eve, Adam is a lonely soul;
(3) be Adam's mate, since without Eve and the first family, Adam will be like a bull unable to procreate offsprings and we are not here to discuss the very question;
(4) symbolize the union between Church and Christ, since the book of Ephesians clearly teaches this remarkable mystery.
(5) exhibite God's glory more completely, since without Eve, a man will not adequately reflect God's glory, as if the triune God's perfect glory is most abundantly reflected by the totality of trinity.