Couples in the context of Genesis 2

The man and his wife were both naked, but they were not ashamed.

Genesis 2:24 NET (emphasis mine)

And God Almighty and Perfect created man, the original human being. But His original creation had a tiny detail: he was neither man nor woman, he was Adam. God hadn't created woman, so how could He create a gender-differentiated being if there was no other one with whom he could couple.

He put the man in this beautiful garden, where Adam saw trees and their fruit, and those were pleasant to look and good for food. The man felt they were good, he naturally knew it, that's why they were pleasant; there was something in him that knew he could eat from them. And then God gave him the freedom to eat from any tree, but the one in the middle.

Then God saw something: the man was by himself, alone but not in the sense of loneliness, God was with him. The Hebrew word that's been translated as "companion" in many bible versions actually means "helper", "one who does what we cannot do by ourselves". If analysed in the context, we see that after that realization, God wanted to create a helper, a companion for man that would help him with the labor God entrusted: to care for the garden. 

But it wasn't going to be any creature that Adam could find the one who was going to be his companion, it had to be one suited for him, complementary to him, not in the context of sexuality --the man was not gender differentiated yet, so that companion wasn't a sexual one. That's why, in order to find a partner for Adam, God brought before him all kinds of animals. There's an interesting thing here: God brought all these creatures before Adam for him to choose. God could've made a perfect companion right away and give it to Adam, but instead He delegated that responsibility to man. 

The Scriptures say that after naming all creatures, a suitable companion was not found, so we can deduce that God and Adam expected to find one among the creatures. He didn't, so God made woman and brought her to him. When Adam saw her, he said "this one at last [...]". After all, God did made him an adequate companion because Adam was happy with it, he saw she was suitable, she was like him, related to him, thus he gave her a name.

It is because all that that the man leaves his parents' home and comes to live with his wife and make a family, because Adam was pleased with the companion that was made for him (the scholars of the NET bible translation agree that the word flesh at the end of verse 24 really means 'kin' or 'family', as explained by the ancient OT custom of calling relatives flesh of my flesh). God knew what he needed and he liked it because it was the woman the one who was made for the man, not the other way around (1 Corinthians 11:8-9). I think that also explains why Jesus said that eunuchs don't have to live with women (Matthew 19:10-12): if they don't find them suitable companions, they don't have to deal with them.

Some times I wonder, if the man had found dogs to be better help for him, women would've never existed, and it would be just Adam and his dogs the ones running the world! So, Genesis 2 is not a story of romantic love, how sex came to be, or other fleshy things, but one of partnership, about finding someone suitable to be our complement, someone like ourselves with whom have a lot of offspring that could help us run the planet. Let's remember this all came to happen so we could accomplish God's very first commandment to Adam: "take care of my garden."