What's going in with Agag?

Saul brings up the capturing of Agag, but offers no explanation for this curious omission from the ban. The reader is thus left guessing as to what the reasons are for this sparing of the Amalekite king. On the one hand, Saul is not at all ashamed or sorrowful because of this act, prompting one to wonder whether Agag also was intended to be sacrificed before YHWH at Gilgal. On the other hand, if anybody was most responsible for the behavior of Amalek, it was presumably their king, and thus one would expect him to be the prime candidate for the implementation of the ban. It is curious that in the previous chapter Saul was ready to kill his own son, yet here he is not willing to kill the Amalekite king, the head of the “sinners, the Amalekites.”—The Unfavored, page 165