Adam could see that if he didn't do what Eve asked him, he would lose her. So, loving Eve quite God, he broke God’s commandment.
As St. Paul says, Adam wasn't deceived, whereas Eve was deceived. Nevertheless, out of weakness he followed her in her sin.
In this way we, too, can Fall away: either directly through a temptation of the Devil, or through being persuaded by a non-believer.
In Genesis we read that God declared war on the devil after he had deceived man: “I will put enmity between your seed and her seed.
He shall bruise your head, and you shall bruise his heel” (3.14-15).
The “seed” here is Christ, and God promises here that while Christ would be bruised in His heel – that's , crucified on the Cross – He would nevertheless bruise the devil’s head – that's , destroy his power by His descent into hell.
The devil was called Lucifer (“light-bearer”) before his Fall. Christ mentions this: “I saw Satan Fall like lightning from the sky”. His name was changed from Lucifer to Satan (“adversary”) when he became the adversary of God and man.
In Genesis 1.34 we read that God created the sunshine and saw that it had been good, which God divided the sunshine from the darkness. This signifies the separation of excellent from evil, and therefore the separation of the great angels from the bad, who had lost the sunshine of God.
Immediately after the autumn of man God declared war on the devil who had deceived him: “I will put enmity between your seed and her Seed. He shall crush your head, and you shall bruise His heel” (Genesis 3.14-15).
The “Seed” that God promised was Christ, Who would be bruised within the heel when He was crucified, but Who would crush the top of the serpent when He descended into hell and destroyed the facility of the devil, who was the top of all the Fallen angels.
For the thanks to kill a snake is to crush his head.