"And I will put enmity [warfare] between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel."
- Genesis 3:15

From From Omega Frequency: Episode 8 (9:45):

After Satan caused man to fall into sin in the garden of Eden, God enacted a plan to save mankind. In Genesis 3:15 we see God will use the seed, or the offspring of the woman, to defeat and destroy the devil. That would happen when Jesus is physically born through the line of Eve. Now when Satan heard that, he realized he had a problem. God had just decreed his defeat, and unlike a lot of Christians who doubt the power and authority of God's Word - Satan most definitely does not.

So he asked himself, how do I stop this from happening? You just can't go and take on God head to head. He tried that and utterly failed. Maybe he could try to kill Eve, but God said it was Eve's destiny to start the bloodline of the Messiah, so he could not touch her. The only thing he could try to do was corrupt the DNA of mankind, so the Messiah could not be born. He could also try to make the world a dangerous and violent place. If he could not kill Eve maybe he could kill off some of the children of Adam and Eve like he did with Cain and Able, and he could use the seed of his fallen ones to do it.