Why was man made from the dirt and woman from the man?
There are several ways to tackle this question.
I like Peter Lombard's explanation: "The woman was created not from just any part of the man’s body, but from his side. This was to demonstrate that she was made for loving communion with him. She was not taken from his head that she might rule over him or from his feet that she might be his slave"
Matthew Henry echoed this: "The woman was made of a rib out of the side of Adam; not made out of his head to rule over him, nor out of his feet to be trampled upon by him, but out of his side to be equal with him, under his arm to be protected, and near his heart to be beloved."
While the explanation given by Lombard and Henry is helpful in capturing the equal-but-different dynamic we see with men and women in Scripture, much more can be said.
Werner Neuer gives a functional explanation of the modes of creation for the man and woman in his book Man and Woman in Christian Perspective (p. 70f):
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The difference in nature between men and women becomes clear in Genesis 2 in the different way God creates them. The man is formed out of the earth (v. 7), but woman is created out of man's rib (vv. 21-2). The different ways of creating man and woman are closely related to their different tasks, which they fulfil in creation according to Genesis 2-3. The man is formed from the soil, whose cultivation is entrusted to him by God (Gen 2:15;3:17), while the woman is created quite differently, out of man's rib, to be his helper. This is her God-given task in life (Gen 2:18). The appointed tasks of the sexes are as basically different as the ways in which they were created by God. Their different modes of creation are intimately related to their tasks in life. It is worth noting that Genesis 2 and 3 in their own language make clear the very different world-outlooks of the sexes, which we have already met in the anthropological-psychological part of this book (Chapter 4, section 3). While the man has an immediate relationship to the world of things, the woman is primarily directed to the world of persons (i.e., in the first instance to her husband).
Further investigation of Genesis 2 and 3 confirms this interpretation. In addition to the man's task of food production through cultivating the ground and the woman's task of being man's helper, another task of the man and the woman is mentioned which confirms the greater thing-related outlook of the man and the stronger personal attachment of the woman. In Genesis 2:19-20 the man is commissioned to name the animals: Giving a name is more than labeling: it is ‘an act of appropriate ordering, by which a man intellectually involves organising conceptually the space which surrounds Adam. According to ancient ideas the nature of something is expressed by its name: Naming the animals help to achieve a mental grasp of their character. It is only the actual expression of a previous inward interpretative appropriation:215 We see this very well in Adam's inventing of the words ish for man and ishshah for woman, which expresses both the difference in nature between the sexes as well as their similarity.
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Neuer’s entire section on this is worth reading. His point is that the way the man and woman were made explain their natures and their different orientations to the world and to each other. Origin explains nature. Origin explain orientation. If you ever wondered why 85% of engineers are men and 85% of elementary school teachers are women, Genesis 2 explains it. Or if you wondered why boys play in the dirt and girls play with dolls, or why most explorers/inventors are men while most nurses and social workers are women – again, this explains it. If you ever wondered why men like books and movies that are mission oriented and women like "chick-flicks" or rom-coms, Genesis 2 holds the key. Men are oriented to the world of things, focused on transforming the raw material of creation into a civilization. The man is built for this kind of work, physically, intellectually, and psychologically. He was made to tend to the earth from which he was taken. Likewise, the woman was made from and for the man. She will tend to him the same way he tends to the garden. She is especially relationally oriented. Physically, emotionally, and psychologically, she is made for nurturing. Obviously, these orientations are not absolute -- men have relationships too, and woman have dominion oriented tasks as well. People cannot be completely fitted into neat and tidy boxes. But the generalizations Scripture gives us about men and woman are important to recognize; there can be no sexual wisdom without them. Genesis 2 shows that the man and woman are different from the very moment of creation; the sexual differences between men and women may vary in expression from one culture to another, but they are rooted in creation and will never be eradicated.
We see these sexual differences spelled out further in the sex-specific curses handed down after the fall in Genesis 3, as the man and woman are each punished in their particular domains. In a fallen world, as the man works the earth to provide for himself and his family, he will have to deal with thorns and thistles. His dominion project is made much harder by the entrance of sin and death. Likewise, the woman will experience the curse most especially in her unique callings as a wife and mother. She will now experience pain in those relational areas that hurt her most – in her marriage and in her child-bearing role.
The words used for the man and woman in Genesis 2 are important. The initial name for the man, “Adam,” means “dirt” or “dust.” The word for the woman at the end of Genesis 2 is “ishshah” which derives from the Hebrew word for “fire.” In the OT, altars are made of earth/dirt (Ex. 20:24) and the sacrifices are set on fire on the altar. Every sacrifice at the tabernacle/temple brought together earth and fire – and thus recalled the original bringing together of the first man and woman – “adam” and “ishshah.” There is a reason we describe Christian/church weddings as taking place at the altar – in the Bible that’s where earth and fire, masculine and feminine, man and woman, are joined. This imagery is all over Scripture. For example, the Lord’s Supper brings together earth (bread) and fire (wine) (Heb. 13:10). And so on.
Consider Genesis 2 in a little more detail. God formed the man from the earth. “Adam” is made from “adamah” (Gen. 2:7). God got his hands dirty in making Adam. Adam is dirt, given life by God’s Spirit. Then God puts Adam in a death-like sleep, cuts open his side like a sacrifice, and then forms the woman out of his rib. When Adam was raised, resurrection-like from his death-like sleep, God presents to him his bride. The Lord gives away the first woman to the first man in the first wedding. When the man sees her, his heart is set aflame with love, so he renames himself “ish,” meaning “flame” or "fire," and he sings a song to his bride whom he names “ishshah," a play on the Hebrew word for fire. In other words, when the man is united to the woman in marriage, he becomes Fire-Man (“ish”) joined to Fire-Woman ("ishshah"). She will be his glory (1 Cor. 11) because fire is certainly more glorious than dirt and in marrying her he becomes a more glorious version of himself as he transitions from being Earth-Man to Fire-Man, from “adam” to “ish.”
A final note on the creation of the woman. The woman is the last creature made by God. She is eschatalogical. She completes the man and the creation. Or to be more precise, creation is complete when the man and woman are joined together. The six days of creation in Genesis 1-2 culminate which a wedding. Paul tells us in 1 Cor. 11 that the woman is the glory of the man. This means many things. Obviously it means she brings light and beauty into his life that would otherwise be lacking. But women do more than decorate the world. She takes whatever the man gives her and glorifies it, which he in turn receives back from her. James Jordan has explained how this works with a series of examples: The man gives his wife a house and she makes it into a home. The man gives his wife a bag of groceries and she turns them into a feast. The man gives her his seed and she gives him a child in return. Everything he gives to her, she returns to him in a more glorious way. This is a sign of her position as the final and most glorious of God's created works. She reveals the future, the glorious goal of history. This is not to say feminists are right when they say "The future is female" because they are missing the key piece. The future is not female; the future is marital. The goal of history is the union of groom and bride. While the pattern of history was first revealed in Adam and his wife, the final goal of history is found in the union of Christ with his bride, the church. That union is the ultimate glory of creation (Rev. 21-22). And that is a glory we should seek to picture and preview in our marriages in the present.