John Piper asserts women were made, right from the start, to represent the church, and man to represent Christ. (Why his view is logically untenable can be found here.)
Let us suppose that from the creation story, one of the two is a character who need rescuing (representing humanity, the church), and the other came down to rescue (representing Christ).
Who, in creation, has a problem? “It’s not good for a man to be alone…” The man has a problem. Who, in the Christ – church picture, has a problem? We do, not Christ.
What help is sent for the man? An ezer k’negdo*, a help meet for him. Ezer translates as helper, but not as in assistant. Almost every time it is used in the Bible, it refers to God helping humans, a strong, rescuing help you cannot do without. In the Christ – church picture, Christ is the helper, the strong, rescuing help you cannot do without.
Next to ezer is k’negdo (meet for him), which mean “opposite him” or “facing him.” The ezer, which denotes the strong superior helping the weak inferior, is brought down with this word to be on eye-to-eye height with the needy man. The analogy, like any other, is far from perfect, but Christ is the strong Savior who became a human for our sake.
Man took Eve’s company, and the church took the salvation offered by God.
Who represents Christ in the creation story? Eve does. And who represents the church? The man does. If marriage is a picture of Christ and the church (I do not call it that), should one partner always be Christ, and the other always the church?
*Not every source transliterates k’negdo the same. Some write it as kenegdo or neged.