Why did Amaziah go to war with Israel?

Kings gives no reason for the challenge itself. It says only that after Edom, "Amaziah sent messengers to Jehoash" (14:8), saying, "Come, let’s look one another in the face" (14:8), and it gives Jehoash's reading of it: "You have indeed struck Edom, and your heart has lifted you up" (14:10). 2 Chronicles tells more in its own account. There Amaziah had hired "one hundred thousand mighty men of valor out of Israel" (2 Chronicles 25:6), sent them home at a man of God's word (2 Chronicles 25:7-10), and they "fell on the cities of Judah from Samaria even to Beth Horon" (2 Chronicles 25:13). After the Edomites, "he brought the gods of the children of Seir, and set them up to be his gods" (2 Chronicles 25:14), and of his refusal to listen Chronicles says, "for it was of God, that he might deliver them into the hand of their enemies, because they had sought after the gods of Edom" (2 Chronicles 25:20). Kings doesn't tell these things. Chronicles also says of his verdict, "He did that which was right in the LORD’s eyes, but not with a perfect heart" (2 Chronicles 25:2), where Kings says "yet not like David his father" (14:3). The two accounts are set side by side here, and nothing more is added.