Bible writers are confused over this. In one place it would say 'the sins of the father will be poured out on the offspring to the third and fourth generations' and in another place it would contradict it, as given in Deut 24:16; Eze 18:20.
Not really confusing. The phraseology is different. Ezekiel 18: 20 specifically states that we are only punished for our own sins, not those of our fathers. So then, how are fathers' sins "poured out" on future generations?
Back then (and now) usually gross sin had to do with idolatry (in one form or another) and ran in families. I was a third generation JW on Dad's side and 4th generationon my Mom's side. The idolatrous sins of my fathers in worshiping a NY corporation got poured out on me. I GREATLY suffered because of their idolatry.... which later became mine.
Most here can testify that the Lack of love, robotic mechanical upbringing, & social dysfunction, led to drug, alcohol, failed marriages and a number of other self-destructive behaviors and ideologies that in turn get passed onto new generations. Multi-generational or Trans-generational Trauma is well known & studied today.
Idolatry is very hard to get rid of once ingrained in a family. It is rarely pretty or easy. It has not been pretty or easy in my personal experience.
Piper has this to say:
1. The sins of the fathers are punished in the children through becoming the sins of the children.
I the Lord...visit the iniquity of the fathers on the children to the third and the fourth generation of those who hate me, but showing steadfast love to thousands of those who love me and keep my commandments.” (Exodus 20:5; cf. Numbers 14:18)
The generations to come who experience the penalty of the fathers’ sins are those who hate God. We are not told how the fathers’ sins become the children’s sins. But what we are told is that when the father’s sins are visited on the children it is because the children are really sinful. That is the form in which the fathers’ sins are visited. Therefore, all judgment is really deserved by the person who is punished.
2. Because of God’s grace, which is finally secured by Christ, the children can confess their own sins and the sins of their fathers and be forgiven and accepted by God.
But if they confess their iniquity and the iniquity of their fathers...if then their uncircumcised heart is humbled and they make amends for their iniquity, then I will remember my covenant with Jacob” (Leviticus 26:40-42).