John Piper said (bold mine):
So when God created man and woman he made us the way we are — with the differences of manhood and womanhood — so that we would be suited for these complementary roles (and for the other expressions of complementarity outside marriage). In this drama man was meant to play the role of Christ, and the woman was meant to play the role of his bride the church.
And we have stressed for five weeks now that these differences are not the result of sin. … Before sin ever entered the world God ordained and fitted Adam to be a loving, caring, strong leader for his wife Eve. And before sin entered the world God ordained and fitted Eve to be a partner who supports and honors that leadership and helps carry it through…
Firstly, a question: Is Piper teaching that God wanted humans to sin, so he made one of the two to exemplify a repentant sinner?
Then, an observation:
Piper says in a world without sin, without man or woman, a man was made to exemplify the redeemer from sin, and a woman to exemplify the sinners who get redeemed. God did not make man play the role of the Redeemer because of sin, nor did women have to play the role of the redeemed because of sin. Even if nobody ever sinned, it would still have been right to let the man play the role of the Redeemer from sin, and the woman of the redeemed.
You could as well tell me the TV was invented in order to show a documentary of the negative effects too much TV has; because the inventor wanted to keep people from watching too much TV.