Our Gemara on Amud Beis discusses the evil plans that the Serpent had for Adam and Chava, namely to eliminate Adam as his rival. His plan was to incite Chava to eat from the forbidden Tree of Knowledge, which would lead her to giving Adam to eat as well. Adam would die as result, so he can have Chava all to himself.  The Maharsha raises the obvious question:  If Chava ate from the forbidden tree, would this not also result in her death? In that case, how would the serpent's plan actually succeed?  The Maharsha answers, as far as the serpent was concerned, he believed that since Chava was only created after the command was given to Adam, she was not subject to its requirements, or at the very least its penalties.

While this is a clever answer, I believe by being honest about the irrational nature of passions, and studying the lessons of an interesting story in Tanach, another explanation is possible. Shlomo Hamelech is confronted with the dilemma of two women, each one, claiming that the live baby is theirs, and the dead baby is the others. He proposes a test of sincerity: (Kings II:3) 

וַיֹּ֣אמֶר הַמֶּ֔לֶךְ זֹ֣את אֹמֶ֔רֶת זֶה־בְּנִ֥י הַחַ֖י וּבְנֵ֣ךְ הַמֵּ֑ת וְזֹ֤את אֹמֶ֙רֶת֙ לֹ֣א כִ֔י בְּנֵ֥ךְ הַמֵּ֖ת וּבְנִ֥י הֶחָֽי׃

The king said, “One says, ‘This is my son, the live one, and the dead one is yours’; and the other says, ‘No, the dead boy is yours, mine is the live one.’ 

וַיֹּ֥אמֶר הַמֶּ֖לֶךְ קְח֣וּ לִי־חָ֑רֶב וַיָּבִ֥אוּ הַחֶ֖רֶב לִפְנֵ֥י הַמֶּֽלֶךְ׃ 

So the king gave the order, “Fetch me a sword.” A sword was brought before the king, 

וַיֹּ֣אמֶר הַמֶּ֔לֶךְ גִּזְר֛וּ אֶת־הַיֶּ֥לֶד הַחַ֖י לִשְׁנָ֑יִם וּתְנ֤וּ אֶֽת־הַחֲצִי֙ לְאַחַ֔ת וְאֶֽת־הַחֲצִ֖י לְאֶחָֽת׃ 

and the king said, “Cut the live child in two, and give half to one and half to the other.” 

וַתֹּ֣אמֶר הָאִשָּׁה֩ אֲשֶׁר־בְּנָ֨הּ הַחַ֜י אֶל־הַמֶּ֗לֶךְ כִּֽי־נִכְמְר֣וּ רַֽחֲמֶ֘יהָ֮ עַל־בְּנָהּ֒ וַתֹּ֣אמֶר ׀ בִּ֣י אֲדֹנִ֗י תְּנוּ־לָהּ֙ אֶת־הַיָּל֣וּד הַחַ֔י וְהָמֵ֖ת אַל־תְּמִיתֻ֑הוּ וְזֹ֣את אֹמֶ֗רֶת גַּם־לִ֥י גַם־לָ֛ךְ לֹ֥א יִהְיֶ֖ה גְּזֹֽרוּ׃ 

But the woman whose son was the live one pleaded with the king, for she was overcome with compassion for her son. “Please, my lord,” she cried, “give her the live child; only don’t kill it!” The other insisted, “It shall be neither yours nor mine; cut it in two!” 

וַיַּ֨עַן הַמֶּ֜לֶךְ וַיֹּ֗אמֶר תְּנוּ־לָהּ֙ אֶת־הַיָּל֣וּד הַחַ֔י וְהָמֵ֖ת לֹ֣א תְמִיתֻ֑הוּ הִ֖יא אִמּֽוֹ׃

Then the king spoke up. “Give the live child to her,” he said, “and do not put it to death; she is its mother.” 

וַיִּשְׁמְע֣וּ כׇל־יִשְׂרָאֵ֗ל אֶת־הַמִּשְׁפָּט֙ אֲשֶׁ֣ר שָׁפַ֣ט הַמֶּ֔לֶךְ וַיִּֽרְא֖וּ מִפְּנֵ֣י הַמֶּ֑לֶךְ כִּ֣י רָא֔וּ כִּֽי־חׇכְמַ֧ת אֱלֹהִ֛ים בְּקִרְבּ֖וֹ לַעֲשׂ֥וֹת מִשְׁפָּֽט׃    

When all Israel heard the decision that the king had rendered, they stood in awe of the king; for they saw that he possessed divine wisdom to execute justice.

Many years ago, I heard a public lecture from  Rav Aharon Soloveichik, who while quoting Freud, observed the following about this story. He said, and I paraphrase from memory: People think the proof of who the mother was came from the selfless act of sacrifice that the true mother made, being willing to give up her own child in order that he live. However, there is another aspect of the story. Freud tells us that the instinct for hatred is even stronger than the instinct for love. Shlomo realized that only a woman who is angry, and filled with hate and jealousy at the loss of her own child could consider having another child cut in half. So Shlomo realized who the real mother was by process of elimination, because the other mother filled with rage and hate must have been the one who lost a child.

So, too, we might consider that the serpent was so consumed with jealousy and rage, wanting Chava to himself, that he barely could consider the fact that he would end up killing her too. This is what happens when our emotions of jealousy, rage and sexuality run unchecked. We are capable of destroying everything, even the objects of our own love and desire.