We discover Saul's failure and the reason that his crown will not be handed down to his own son. Israel is preparing for war with the Philistine's. They are awaiting Samuel, the high priest, to come and offer a sacrifice to God and bless the Israelite effort. When Samuel is late in arrival, Saul takes matters into his own hands and offers the sacrifice himself. Remember that this duty has been reserved for the Levites since the time of Moses. Not only does he usurp the role of the Priest but when Samuel arrives he blames his offense on Samuel. His sin is compounded by his arrogance and refusal to admit his sin. Remember this was the sin of Adam and Eve as well as they blamed others for their failure. Samuel tells Saul that God is looking for a man after his own heart thus telling us well in advance that Saul's days as king are limited. Remember those words, "a man after God's own heart" as we are introduced to a shepherd boy named David in future chapters.
We are introduced to Saul's son Jonathon. Jonathon exhibits some of those characteristic that endeared him to David. He was brave and valiant, a great warrior and leader of men. He engages the Philistines in battle and slays many causing the rest of the Israelite army to join in the routing of the enemy. Saul again violates God's will be failing to be obedient to the instructions to dedicate the enemy and the spoils to God. (remember Jericho) When Samuel asks about the failure, Saul blames the men for keeping the best of the stock, etc. Again he is unable to be repentant of his own sin. Samuel tells Saul he is done with him. He cannot help him if he is unable and or unwilling to confess his sins before God.
The destruction of the Amalekites had been ordained back in the days of Moses when they had attacked the Israelites after they had left Egypt. (Exodus 17) Using Saul to accomplish this task was a further test of Saul's ability to be obedient to God's will. What test is God using to ascertain our loyalty? Saul set up a monument to himself. How audacious and certainly a violation of God's call to have no other God's. Saul fails to honor God and to give God glory for his victories. Pride and disobedience are part of Saul's character. God rejects Saul and regrets his selection of a King. Samuel grieves over Saul and laments what lies ahead