Contradiction with Deuteronomy 17:15
Deuteronomy 17:15 states that the Israelites should only set a king over themselves whom God has chosen, while 1 Samuel 10:17 involves the people themselves deciding they want a king, suggesting God's disapproval of their desire for a monarch.
Deuteronomy 17:15: Thou shalt in any wise set [him] king over thee, whom the LORD thy God shall choose: [one] from among thy brethren shalt thou set king over thee: thou mayest not set a stranger over thee, which [is] not thy brother.
Contradiction with 1 Samuel 8:7
In 1 Samuel 8:7, God tells Samuel that the people's request for a king means they are rejecting God as their king, while 1 Samuel 10:17 is part of the process of setting up a human king, which indicates a contradiction in God's acceptance of their request.
1 Samuel 8:7: And the LORD said unto Samuel, Hearken unto the voice of the people in all that they say unto thee: for they have not rejected thee, but they have rejected me, that I should not reign over them.
Contradiction with Judges 8:23
Judges 8:23 has Gideon refusing kingship by stating that the Lord shall rule over the people, contrasting with 1 Samuel 10:17 where the narrative progresses towards the establishment of a human king.
Judges 8:23: And Gideon said unto them, I will not rule over you, neither shall my son rule over you: the LORD shall rule over you.
Contradiction with Hosea 13:11
Hosea 13:11 describes God expressing displeasure by saying He gave the Israelites a king in His anger, which stands in contrast to the proceedings of appointing a king in 1 Samuel 10:17.
Hosea 13:11: I gave thee a king in mine anger, and took [him] away in my wrath.