It was clearly ADAM'S disobedience to God's command not to eat the fruit from the Tree of the Knowledge of Good and Evil that caused the Fall and brought sin into the world. It was not through anything Eve did. Paul named Adam as the perpetrator in his epistle to the Romans. Paul echoes this in 1 Corinthians.
Romans 5:12-21--Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned— for until the Law sin was in the world, but sin is not imputed when there is no law. Nevertheless death reigned from Adam until Moses, even over those who had not sinned in the likeness of the offense of Adam, who is a type of Him who was to come.
But the free gift is not like the transgression. For if by the transgression of the one the many died, much more did the grace of God and the gift by the grace of the one Man, Jesus Christ, abound to the many. The gift is not like that which came through the one who sinned; for on the one hand the judgment arose from one transgression resulting in condemnation, but on the other hand the free gift arose from many transgressions resulting in justification. For if by the transgression of the one, death reigned through the one, much more those who receive the abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ.
So then as through one transgression there resulted condemnation to all men, even so through one act of righteousness there resulted justification of life to all men. For as through the one man’s disobedience the many were made sinners, even so through the obedience of the One the many will be made righteous. The Law came in so that the transgression would increase; but where sin increased, grace abounded all the more, so that, as sin reigned in death, even so grace would reign through righteousness to eternal life through Jesus Christ our Lord.
1 Cor 15:20-24--But now Christ has been raised from the dead, the first fruits of those who are asleep. For since by a man came death, by a man also came the resurrection of the dead. For as in Adam all die, so also in Christ all will be made alive. But each in his own order: Christ the first fruits, after that those who are Christ’s at His coming, then comes the end, when He hands over the kingdom to the God and Father, when He has abolished all rule and all authority and power.
