It is not clear why a comparison is made to divination and idolatry. Possibly Saul’s rebellion was an attempt to manipulate God (which is what happens in divination). He disobeyed the Lord’s direct command, but since it was followed by sacrifice he was assured of mercy. This allowed him to get what he wanted, namely the approval of his men (1 Samuel 15:30).
With arrogance and idolatry, the connection is clearer. By thinking that he was a law unto himself and did not have to submit to the Lord,1 Saul had rejected the Lord as God and placed his own opinion above that of the Lord.
23 For rebellion is as the sin of divination, and presumption is as iniquity and idolatry. Because you have rejected the word of the LORD, he has also rejected you from being king.”