In the beginning God created man and saw it was not good for him to be alone. So God brought forth to Adam all the animals on the earth, and after naming them, Adam saw that none were a suitable partner for himself. So God put Adam into a deep sleep, opened his side, removed a rib, and fashioned from it woman as a bride for Adam.
On Good Friday, God saw that it was not good that man should live burdened by sin and separated from the love of the Trinity. And so seeing that the law of Moses was not a suitable path for man's salvation, Christ offered Himself in love on the cross, on the hill of Golgotha where tradition says Adam was buried. And during the "deep sleep" of death, Christ's side was opened by a lance, and through the blood and water that flowed out, Christ the New Adam fashioned for Himself His own bride, the Church.
God created Eve to complete Adam; God created the Church so that He could complete man through relationship with Himself.