Genesis 1: 27 And God created man in His own image, in the image of God created He him; male and female created He them.
Adam begins as a dual entity male and female. In this sense it is Elohim the maker of all things that conceives Adam out of the reflection from above, the image of holiness and its expression
Gen 2: 18 And the LORD God said: 'It is not good that the man should be alone; I will make him a help meet for him.'
Was Adam alone? Male and female were created together. A singular entity with a dual nature. In order for this to happen another element is introduced. It is now the dual nature of God, YHV"H ELHY"M.
Gen 2: 21 And the LORD God caused a deep sleep to fall upon the man, and he slept; and He took one of his ribs, and closed up the place with flesh instead thereof.
Out of man comes woman via one of the ribs.
Gen 2:23 And the man said: 'This is now bone of my bones, and flesh of my flesh; she shall be called Woman, because she was taken out of Man.'
Adam realizes that even there is an appearance of separation Woman is intimately a part of him never to be separated.
At this point the harmony of man and woman are complete. What has happened here is no so much their separation but the realization that woman is attached to man irrevocably.
Think about this in terms of consciousness. You have an idea. In order for this idea to soar grow and transform itself into its expression you have to be united with your creative nature, your inner connection. In Kabbalistic terms Shekhinta and Kudsha Brikh Hu have to be united.This is an ongoing process.
Whenever there is any kind of artificial separation as in that imposed by the rules of society that seeks to separate, subjugate, or in any way limit the freedom of woman to become as one with man then that is what is called the Exile or galus. Therefore when you see the separation of women in any form whatsoever you will understand that it is because of the misguided attempts by man to control woman.
It is encouraging to see the ongoing letting go of those proscriptions against women since our society as a whole can only move forward with woman fully emancipated. Think of what has happened during the past one hundred years as more and more women have a chance to express themselves adding to the general richness of society. Still there are the orthodox throwbacks that seek to maintain the status quo using various self serving rationalizations. These too must fall by the wayside since the reunification of Adam in inevitable. It is inevitable since it is built into the master plan that even the most devout must come around to. When this comes to pass as it surely must the awesome woman will once against be restored to her rightful place an integral part of man unified together with the Creator.