Thinking about the Serpent, Adam, and Eve

I been thinking about the story of the fall of Man. Adam and Eve took the fruit of the tree they where instructed to not eat from. We all should know the story very well. Adam was standing with Eve during her conversation with the serpent and he never stopped her. So they really are both at fault for the mistake that was made. They wanted to gain knowledge, and saw the fruit looked good to their eyes.
There is something I never really thought about in Genesis. Genesis 2:20 ” So the Person gave names to all the livestock, to the birds in the air and every wild animal. But for Adam there was not found a companion suitable for helping him.
When someone names something they have authority over it. G-d named Adam, so G-d had the authority over Adam. When G-d had Adam naming the animals this is something I never realized Adam would have control or authority over the creatures of the Earth. He named them. While Adam was naming the animals it was noticed there was a help mate for him. So G-d put him to sleep. He named her too, but I think the authority was a little different then what we think of it now. Adam would have treated her the Same way G-d had treated him because he would have only had G-d example to go by.
In chapter 2 this is where Adam and Eve both get deceived by the enemy and eat the fruit.
Genesis 3:1 Now the Serpend was more crafty than any wild animal which Adonai G-d had made, he said to the woman. “Did G-d really say ” you are not to eat from any tree in the garden”?
We see Eve adding to what G-d instruction were, and we see that her and Adam or both being temped. They never took the control which G-d gave them over the creature over devil who was in the snake. I never really thought about this until recently. Sometimes we allow things which have no control over us to take the control, we are blinded to the truth or what is really happening.
It kind of like trying to find treatments for acne some of them are great at fighting off what causes acne and some of it just makes matters worst. I wonder how different it would have been if Adam had taken the control over that serpent and told it to leave.