Both of the Genesis accounts demonstrate the awesome potential of earthlings by indicating that they can and need to aspire to be "like God." More importantly, the second narrative says nothing about the “likeness to God” prior to the eating from the special tree in the center of the garden: “God knows that when you eat of it your eyes will be opened, and you will be like God, knowing good and evil” (Gen 3:5). Becoming "like God" here is an awakening of our interior capacity for making discoveries and for discerning what is good and evil. This is what our Parent does! And, now, this is what God enables his children to do in imitation of God.
In the classical theological tradition, Gen 2-3 narrates the process whereby Eve discovers her calling to be "like God." The importance of divinization (theosis) in Roman Catholic teaching is evident from what the Catechism of the Catholic Church says of this:
The Word became flesh to make us "partakers of the divine nature": "For this is why the Word became man, and the Son of God became the Son of man: so that man, by entering into communion with the Word and thus receiving divine sonship, might become a son of God." "For the Son of God became man so that we might become God." "The only-begotten Son of God, wanting to make us sharers in his divinity, assumed our nature, so that he, made man, might make men gods."
Roman Rite liturgy expresses the doctrine of divinization or theosis in the
prayer said by the deacon or priest when pouring a small amount of water into
the wine of the Eucharistic chalice: "By the mystery of this [mingling of] water
and wine may we come to share in the divinity of Christ who humbled himself
to share in our humanity." ("Per huius aquae et vini mysterium eius efficiamur
divinitatis consortes, qui humanitatis nostrae fieri dignatus est particeps"
What Eve acquires through the eating of the Tree of Knowledge is thus what Jesus is able to impart to his disciples. "We come to share in the divinity of Christ" today by way of acquiring what Eve discovered when "her eyes were opened" and she saw herself and her world from God's perspective. Thus, in the beginning, Eve gave to the earthling the ability to be "like God," while today, we gain this ability from Jesus. This is what the Church Fathers meant when they said, "we come to share in the divinity of Christ who humbled himself to share in our humanity."
Eve is thus the physical and spiritual mother of all the living! Once the later Church Fathers condemned Eve as the one who betrayed Adam, the Church elevated Mary, the Mother of Jesus, to become the "new Eve" who accompanied the "new Adam" (=Jesus) in his work of salvation. According to Gen 2-3, however, Eve is the savior who brings salvation (=divinization) to Adam. This will become clearer as you continue to examine and meditate on the text of Gen 2-3 which is before us.
For more details, see Paul M. Collins, Partaking in Divine Nature: Deification
and Communion (NY: Continuum, 2001).