Gen 1:26-28 "And God said, let us make man in our image, after our likeness, and let them have dominion over the fish of the sea and over the fowl of the air, and over the cattle and over the earth, and over every creeping thing that creepeth on the earth. So God created man in his image, in the image of God created he him; male and female created he them. And God blessed them and God said to them be fruitful and multiply and replenish the earth and subdue it and have dominion over the fish of the sea and over the fowl of the air and over every living that moveth on the earth"

Man can be both male and female. Here it is both (male & female, created them, blessed them, said to them, multiply indicates both)
God's image = resemblance, representative figure
Likeness = model, shape, similitude, like manner, one who is similar, a counterpart
Counterpart = someone precisely or closely resembling another, one who supplements or completes another, a compliment.

Gen 3:8 God walked and talked with Adam in the cool of the day. Adam here again refers to both woman and man. God gave the same image and likeness to both.

He did not make one image for him and a different lesser one for her. God blessed both equally; He did not bless just the man who was then told to bless the woman under his authority. He told both to subdue earth. Subdue = kabash, tread down, disregard, conquer, subjugate, violate, bring into bondage, force, keep under and bring into subjection.

He told both to have dominion.
Dominion = radah, tread down, subjugate, prevail against, reign or rule over. Had equal power, mental capacity, emotional stability, and physical strength. Both had equal authority.

God was very specific about what was to be subdued and what they were to have dominion over.

There is no reference to man having authority to subdue or have dominion over the woman.

Creation order did not make God's image and likeness less in the woman. Creation order did not make her inferior in position, value, worth, mind, body, soul, and spirit. There was no headship or authority structure in creation. God did not assign anyone to be boss or head over the other.

NOT GOOD FOR MAN TO BE ALONE

After each day God said what he had created was good. Man was created out of dust, God breathed life into him. Gen 2:18 "And the Lord God said It is not good that the man should be alone; I will make a help meet for him."
Not good = not gracious, not kindly, not loving, not pleasant, not prosperous, not in best welfare of, not of value.
Alone = a separation, by imp. A part of the body, apart, by self, each alike divided, solitary. This portrays very lonely, desperate, desolate, incomplete condition.
Help = Ezer or Azar refers to God as one who rescues in time of trouble. Psalm 30:20, 40:17, 46:1, 70:5, 109:26. It means surround, protect, aid, succor. God has a superior power to rescue us when we cannot rescue ourselves. God is not a subservient slave and neither is woman. Woman was created to rescue man from his aloneness that was not good. He knew he could not rescue himself from his aloneness. NOVEL idea!! Woman was created to surround, protect, aid and succor man.
Protect = shield or defend from attack, harm or injury, guard.

Today's theory of man protecting woman is based on an 1800's Victorian view of women, not on Bible fact, however, this does not negate or diminish his role as protector.

I LOVE THE PROTECTION FROM MY HUSBAND

Since man and woman were both created in, the image and likeness of God both have the nurturing power of God to protect, surround, and succor each other. Succor = help or relief rendered in time of danger, difficulty or distress.

Someone who affords relief, goes to aid of or helps, one who rescues. When God created woman FOR man, that was his purpose, it was not to make her a subservient slave. Many say the woman was a helpmate, meaning a helper to do his bidding. The word used is actually a help meet meaning one suitable for him, like him in soul and spirit. Being suitable is prerequisite to being a mate. After the creation of woman, God said it was very good.
Very = God said, "Vehemently NOW it was EXCEEDINGLY WHOLE!
Vehement = fervent, passionate, intense feeling.
Good = beautiful, best, better, graciously, joyful, kindness, loving, precious, prosperous, sweet, this is what creation was before the woman was created.
Exceedingly = greater than usual, surpassing, extraordinary, to a greater degree than usual, extremely. This is what the woman did for creation!
Whole = containing all the parts necessary to make up a total; undivided; undiminished; entire, complete. All the parts or elements entering into and making up a thing, totality. An organization of parts making a unity or system.

This woman was not an after thought to God. He let the man find out what desperate lonely condition he was in, THEN God brought this exceedingly, extraordinary, compliment or counterpart of the man to him. This was no slave, but a rescuer who made the man complete and creation complete. There was absolutely no headship implied or intended by God. God did not give any instructions for a rulership type relationship.

Gen. 2: 21-24 "And the Lord God caused a deep sleep to fall on 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 the man, made he a woman, and brought her to the man. And Adam said this is now bone of my bone, flesh of my flesh; she shall be called Woman because she was taken out of man. Therefore, shall a man leave his father and mother and shall cleave to his wife and they shall become one."

There is headship in these verses but it is NOT an authoritarian, governing ruling, boss-type headship.

Man was formed out of dust.
Formed = squeezed into a shape, molded into a form as by a potter, earthen. Woman was built out of flesh and blood.
Made = built. Built = construct or form by assembling separate parts. Woman could not be made inferior to man in any way, because she was made out of the part that came from Adam. The only way she could be inferior is if the material God took from the man was inferior. If man says the woman is inferior then he is admitting that man himself was inferior. Adam knew exactly what kind of perfection this woman was. He was overjoyed to have her rescue him from being alone.