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The existence of the Trinity is an existence of love. Love, true love, is not satisfied or realized fully unless it is shared. Now, of course, each person of the Trinity loves each other. But the Love of God is a creative love, and He wanted to share His love not only within Himself, but He wanted to express it outwardly, which is why He created everything; the crown of His creation being mankind. Man, being created in the image and likeness of God, is filled with and reflects the Love of God. Since the Love of God is not satisfied unless it is shared, God not only wanted man to share this love with Him, but with someone equal to him. This is why, I think, God created woman for man, so that man could share this love with someone who was his equal, his partner.