What does 1 Samuel 15:20 mean?

Samuel has thoroughly condemned King Saul as doing evil. He failed to obey God's command to kill every living person and animal among the Amalekites (1 Samuel 15:2–3, 19). Saul's response is to double down on his previous excuses and attempts to shift the blame on to those under his authority (1 Samuel 15:15).

The king insists that he did obey God. He went on the mission given to him by the Lord (1 Samuel 15:3). He declares that he brought back the Amalekite king, as if that was part of the mission. He adds that he devoted all the rest of the Amalekite people to destruction, meaning that he is taking responsibility for having all of them except for the king killed (1 Samuel 15:9). But partial obedience is no obedience at all. The king should not have been spared, and Samuel will rectify that later (1 Samuel 15:32–33).

As we often do when confronted about our sin, Saul refuses to accept an honest version of events or accountability for his actions. In the following verse, he shifts all blame onto those under his command, even as he provides an explanation to justify what they did (1 Samuel 15:21). This amounts to Saul denying his responsibility as king, blaming his followers, and then trying to excuse the actions as not sinful to begin with.