There are two possible reasons that Matthew’s genealogy skips the kings Ahaziah, Joash, and Amaziah (1 Chronicles 3:11–12). One is just to simplify the list, as we also see in Ezra 7:3 and 1 Chronicles 6:6. A more significant reason could be that all three kings were killed because of conspiracies connected with their rejection of the Lord. Their deaths foreshadowed the complete ruin of the house of David in the deportation to Babylon.
Between Joram and Uzziah (also known as Azariah, see 2 Kings 15:1, 2 Kings 15:6, 2 Kings 15:8, 2 Kings 15:17, 2 Kings 15:23, 2 Kings 15:27 and 2 Kings 15:13, 2 Kings 15:30, 2 Kings 15:32, 2 Kings 15:34) three generations are skipped: Ahaziah, Joash, and Amaziah (1 Chronicles 3:11–12). Such omissions often occur in Jewish genealogies for the purpose of simplifying them (see Ezra 7:3 and 1 Chronicles 6:6).1
Some explain the omission as follows: the one thing that all three kings omitted from the list have in common is the fact that they were all killed because of conspiracies and those conspiracies were connected to the fact that these kings turned away from the service of the Lord. The omission of the three kings therefore reminds us of a lasting scar caused by the change in course under Joram. The house of David had reigned for centuries, but there is a gaping wound of sin and judgment in the middle of the survey of that history. God had put an end to the lives of the three sons of Joram, but he did not yet put an end to the rule of the house of David. When even the later kings failed to take the admonition to heart, however, their rule finally ended in total degradation. But that also occurred in connection with the past history. The deportation to Babylon certainly did not occur as an abrupt judgment on a family that had otherwise been left alone in peace—quite the contrary.2
7 and Solomon the father of Rehoboam, and Rehoboam the father of Abijah, and Abijah the father of Asaph,