It can hardly be said that there was enmity between Eve and Satan. The Hebrew word used here is 'êybâh, and it connotes real, true hatred. It only appears 4 times in the Old Testament. One is here in Genesis 3:15, another is in Numbers 35:20-24, where it speaks of a person killing another out of enmity.
And if he pushed him out of hatred or hurled something at him, lying in wait, so that he died, or in enmity struck him down with his hand, so that he died, then he who struck the blow shall be put to death. He is a murderer. The avenger of blood shall put the murderer to death when he meets him. "But if he pushed him suddenly without enmity, or hurled anything on him without lying in wait or used a stone that could cause death, and without seeing him dropped it on him, so that he died, though he was not his enemy and did not seek his harm, then the congregation shall judge between the manslayer and the avenger of blood, in accordance with these rules.
Ezekial uses the word twice:
Thus says the Lord GOD: Because the Philistines acted revengefully and took vengeance with malice of soul to destroy in never-ending enmity, therefore thus says the Lord GOD, Behold, I will stretch out my hand against the Philistines, and I will cut off the Cherethites and destroy the rest of the seacoast. (25:15-16)
The word of the LORD came to me: "Son of man, set your face against Mount Seir, and prophesy against it, and say to it, Thus says the Lord GOD: Behold, I am against you, Mount Seir, and I will stretch out my hand against you, and I will make you a desolation and a waste.I will lay your cities waste, and you shall become a desolation, and you shall know that I am the LORD. Because you cherished perpetual enmity and gave over the people of Israel to the power of the sword at the time of their calamity, at the time of their final punishment, therefore, as I live, declares the Lord GOD, I will prepare you for blood, and blood shall pursue you; because you did not hate bloodshed, therefore blood shall pursue you. (35:1-6)
It is a strong word. It does not simply mean dislike, but true and deep hatred. It is used in reference to:
*]Murder perpetrated out of a hatred so pure that it seeks death, a true premeditated hatred, as opposed to a mere flash of anger.
*]The Philistines, who had “malice of soul” to destroy the Israelites. They sought revenge for Israel’s past victories against them, not merely land or power. Their attack was one of unmitigated hatred.
*]The hatred stemming all the way back to the incident of Esau and Jacob, a hatred based merely on an age old grudge, one along the lines of a feud between clans.
*]In all cases, a hatred worthy of death or destruction by the direct intervention of God.
It can certainly not be said that such hatred existed between Eve and Satan. For this to be the case, Eve would have had to be completely opposed to sin. It would not be enough for her to have lived merely like you or I, loving God and seeking Him yet still allowing our selfishness to get the best of us at times. That would not be enmity. Even if we say that neither Eve nor anyone else could possibly be without sin and say that she would not have had to be free of all sins, it is still the case that she would at least have to be in a right relationship with God for it to be said that there was enmity between her and Satan. Mary could have been in a right relationship with God; in fact, I think it is fair to say that she was, given that she bore Him in her womb. Eve, on the other hand, was expelled from the garden the moment that God had finished telling her this. She was cursed, and she was outside of God’s presence. She was not in a right relationship. There was not 'êybâh between her and Satan. There are other Hebrew words that could be much more appropriately used to describe what was between Eve and Satan. In fact, Protestant commentators remark that God’s promise to place enmity between the woman and Satan is itself a prophecy of salvation, insofar as to have enmity with the enemy of God is to have friendship with God. In this prophetic sense the passage would refer to Mary, because this friendship with God was not yet restored to Eve, and therefore the prophecy had yet to be fulfilled until Mary gave birth to Christ.