1. The kingdom of Israel is divided, primarily because of Rehoboam’s harsh leadership.
“Solomon’s kingdom barely outlived him. At his death his son and heir, Rehoboam, sought to ascend the throne of Israel and Judah. There was no difficulty in the south. The elders of Judah were no doubt pleased to anoint another native son to continue the rule which had favored Judah in so many ways. In the north, in Israel, it was a different story altogether. Before there was to be an acclamation of any son of Solomon, there must be some plain talk about certain policies of state which the men of the northern hills and valleys thought discriminatory if not unbearable. Forced labor gangs for royal building projects simply must not continue. Heavy and inequitable taxation favoring Judah would have to be modified. The new king would either have to find other ways to carry out his personal and imperial ambitions or else temper his desires. In any case, the northern tribes were clearly unwilling to bear the brunt of the monarchical burden. Underlying these real grievances was the reviving strength of the tribal elders. Solomon had not completely destroyed their power after all.” (Harry Thomas Frank, Discovering the Biblical World,p. 99.)

1 Kings 12:7 They will be thy servants for ever
‘The way to insure the obedience of the people is to hold the reins of empire with a steady and impartial hand; let the people see that the king lives for them, and not for himself; and they will obey, love, and defend him. The state is maintained on the part of the ruler and the ruled by mutual acts of service and benevolence. A good king has no self-interest; and such a king will ever have obedient and loving subjects. The haughty, proud tyrant will have a suspicious and jealous people, hourly ripening for revolt. The king is made for the people, not the people for the king. Let every potentate wisely consider this; and let every subject know that the heaviest cares rest on the heart, and the heaviest responsibility rests on the head, of the king. Let them therefore, under his government, fashion themselves as obedient children; acknowledge him their head; and duly consider whose authority he has; that they may love, honor and obey him. Happy are the people who have such a king; safe is the king who has such a people.’ (Clarke’s Bible Commentary)
1 Kings 12:8-11 He forsook the counsel of the old men
1 Kings 12:16. What Does the Phrase “What Portion Have We in David? … See to Thine Own House, David” Mean?
‘Those assembled made it clear that they no longer considered themselves to be part of the house of David (Judah). They rebelled against the dominion of Rehoboam and moved to establish their own kingdom. “To your tents” is an idiom meaning “Let’s go home!” (D. Guthrie and J. A. Motyer, eds., The New Bible Commentary: Revised, p. 337; see also 1 Kings 12:19; 2 Samuel 20:1–2; 2 Chronicles 10:16). The northern tribes withdrew their allegiance from Rehoboam and the house of David and said in essence, “David, you take care of your own house. We will no longer be associated nor have an inheritance with you” (see Adam Clarke, The Holy Bible … with a Commentary and Critical Notes, 2:436).’ (Institute Old Testament Manual)

2. Jeroboam and Rehoboam lead their kingdoms into idolatry.
1 Kings 11:38 And build thee a sure house
‘He would have continued his posterity on the throne of Israel, had he not by his wickedness forfeited the promises of God, and thrown himself out of the protection of the Most High.’ (Clarke’s Commentary on the Bible)

1 Kings 13:33-34 Jeroboam returned not from his evil way
‘As for King Jeroboam, verse 33 confirms that he continued to elevate the dregs of society to leadership positions, and verse 34 makes it clear that his idolatry yielded dire results for him and his family. Fulfillment of the prophecy about the destruction of his idolatrous altar is related in 2 Kings 23:15-18.’ (Andrew Skinner and D Kelly Ogden, Verse by by Verse – The Old Testament)