Very interestingly, God also tells the same to Cain:
Genesis 4:7, KJV: If thou doest well, shalt thou not be accepted? and if thou doest not well, sin lieth at the door.
And unto thee shall be his desire, and thou shalt rule over him.
Looks like this isn't about Cain and Abel, but about Cain and sin, however, it's the same sentence, like the curse repeats.
Genesis 4:7, ESV: If you do well, will you not be accepted? And if you do not do well, sin is crouching at the door. Its (sin's) desire is contrary to you, but you must rule over it."
I think here it meant, "the choice is yours", as in, "resist the devil and he will flee".
Then Cain slays Abel.
I don't know why is Adam being exalted over this verse, because even if Eve was deceived, God states that Adam didn't do any better than her. Based from what was said to Cain, it's clear that God was saying to Adam, it was your job to stop her, you knew better than this. Furthermore, Eve admits that she was deceived and sinned, but Adam has the guts to blame Eve and God for what he did "this woman YOU gave me"... etc.
Sorry, doesn't make the case for Adam displaying a stellar or superior behavior... looks more brazen to me.
But Eve was subjected because of what he said, because he blamed Eve and God for his own doings.
I believe God makes Adam the leader, in order to leave Adam without excuse.