There are two possible answers that stand out to me. First, in Genesis 2:15, the Lord God takes the man (’ādām) and places him ‘in the garden of Eden to till it and keep it.’ Humanity (’ādām) has responsibilities; it is to ensure the garden flourishes; and the presence of another from the man (’ādām), an other from the same, the woman (’îššāh) alongside the man (’îš), will enable humanity (’ādām) to fulfil its duties.
The second possible answer is this: given the Lord God’s requirement that the man (’ādām) should not eat from the tree of the knowledge of good and evil (2:17), the man (’îš) needs another – the woman (’îššāh) – to help him resist any temptation to eat from this tree. Perhaps this is why the serpent targets the woman (’îššāh; 3:1). The woman is the man’s helper (‘ezer; 2:17); there is no reason for the man to doubt the woman’s good intentions when she passes him the forbidden fruit (3:6). In much the same way, the woman had no reason to doubt the intentions of the serpent.
Whatever else might be extrapolated from these verses about gender roles and the place of women in ecclesiastical authority and leadership, it seems to clear to me that men and women are to worship (‘to till it and keep it’ evokes the language of temple worship) together and to avoid sin together.