Why did God create a woman?

Because Adam couldn't find a helpmeet among the animals that God created.

And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam there was not found an help meet for him.

And the LORD God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof;

And the rib, which the LORD God had taken from man, made he a woman, and brought her unto the man. Genesis 2:20-22