Eve goofed by talking to the serpent. Adam goofed by not correcting Eve's goof before it became a sin.
Eve didn't talk to the serpent. The serpent talked to Eve.
Adam didn't need to correct Eve. Adam needed to find something else to do.
If it had not been a husband/wife situation, Adam may not have been the one in authority over Eve.
Genesis 3:2,3:
Quote
The woman said to the serpent, We may eat fruit from the trees in the garden, but God did say, You must not eat fruit from the tree that is in the middle of the garden, and you must not touch it, or you will die.
So, even though Eve didn't sin by disobeying a directive from God in her speech with the serpent, she may have lied. Perhaps we don't have the whole conversation that God had with Adam and Eve. Perhaps God did indeed tell them to not touch the fruit. But we don't have record of it.