The Bible Says
Deuteronomy 24:16 Meaning

Fathers shall not be put to death for their sons, nor shall sons be put to death for their fathers (v. 16). In the eyes of the LORD, to do so would be the same as charging an innocent person unjustly with a crime deserving of the death penalty. God gave each person the ability to choose, and each person is to bear the consequence of their own choices.

The principle underlying this law is that everyone shall be put to death for his own sin. The word sin here likely refers to a capital crime committed by someone. So, those in authority were to make sure to punish the guilty person and protect the innocent, even if the innocent person was a close family member. It did not matter how important someone was, if they committed a capital crime they were to be held to account.

How does this correspond with what was said in the second commandment (Deuteronomy 5:8-10)? There, after commanding the people to not make, worship, or serve idols, the LORD said that He is "a jealous God, visiting the iniquity of the fathers on the children, and on the third and the fourth generations of those who hate Me." The answer is that this is a verse that speaks of God's mercy. God provides time for people to repent before imposing divine judgement against idolatry and living in sin against God and His ways. It is only when the children continue the iniquity of their fathers for three to four generations that God eventually intercedes to judge. If a generation repents, then God relents of bringing judgment.

But at all times individuals are to be held to account for sins against one another.

Moses forbade the Israelites from punishing one family member for the actions committed by another member of his family. There were to be no blood feuds. Families were not to be held responsible. Individuals were to be held responsible.

Later in Israel's history, both Jeremiah and Ezekiel restated Moses's principle of individual responsibility because the Israelites who were in exile thought they were suffering because of the sins of their fathers (Jeremiah 31:29-30; Ezekiel 18:14-20). The prophets boldly declared to them that everyone will be punished for his own sins (Jeremiah 31:29-30; Ezekiel 18:14-20). God granted each person the agency to make choices. That is a major part of being created in the image of God. Each person is allowed to make certain choices for themselves, and each person will bear the consequence of their own choices.