The major reason is simple: control.
Reading 1 Kings 12 from the beginning will have the fuller story, upon which the following explanation is based.
Jeroboam may be considered an usurper. God had established David's line as the rightful heirs to the throne. However, Solomon's son Rehoboam, upon ascending to the throne, unwisely accepted the advice of his young counselors, and ignored that of the older ones. The young counselors rashly advised that he be strict, and impose heavier taxes, etc. in order to show and establish his authority.
Ten of the tribes, afterward called the northern kingdom, defected, and selected Jeroboam as their king.
Under the circumstances, Jeroboam could not also be strict, as Rehoboam had been. But he would take no nonsense from the people in terms of their loyalties again vacillating back to Rehoboam. In order to ensure that they would remain his subjects, he imposed restrictions against their return to Jerusalem, where Rehoboam reigned. Jerusalem was both the seat of David's government and the center of worship, having the temple of God, Solomon's beautiful temple, as its centerpiece.
So Jeroboam instituted a number of changes to keep the people from returning to Jerusalem.
- He built the two golden calves, one in Bethel, and one in Dan. Providing two places for worship was a matter of convenience.
Whereupon the king took counsel, and made two calves of gold, and said
unto them, It is too much for you to go up to Jerusalem: behold thy
gods, O Israel, which brought thee up out of the land of Egypt. (1
Kings 12:28, KJV)
He could not force the people to stay out of Jerusalem, but it would be much less distance to travel to one of these than to Jerusalem--making Jerusalem less convenient. The choice of the golden calves was inspired by Aaron's precedent-setting apostasy. Somehow, even error, after steeping with time, appears more attractive, and it is human nature to regard highly something that has been handed down through tradition or history. Thus, the new apostasy met with little resistance, and was quickly adopted by the people.
Howbeit from the sins of Jeroboam the son of Nebat, who made Israel to
sin, Jehu departed not from after them, to wit, the golden calves that
were in Bethel, and that were in Dan. (2 Kings 10:29, KJV)
- Jeroboam also elevated as priests of the high places many among the lowest of the people--the rabble crowd--turning away from the rightful spiritual leaders of the tribe of Levi. It might be on par with turning away from ministers, pastors, or priests today to having churches led by rappers, rock stars, and uneducated high-school dropouts. The change was dramatic.
And he made an house of high places, and made priests of the lowest of
the people, which were not of the sons of Levi. (1 Kings 12:31, KJV)
- He changed the date of Passover celebration, making it a month later. This would, of course, mean that no occasion of consequence would coincide with these new dates in Jerusalem at that same time, reducing any motivation to travel there.
And Jeroboam ordained a feast in the eighth month, on the fifteenth
day of the month, like unto the feast that is in Judah, and he offered
upon the altar. So did he in Bethel, sacrificing unto the calves that
he had made: and he placed in Bethel the priests of the high places
which he had made. (1 Kings 12:32, KJV)
Which God?
If Jeroboam had been motivated by a desire to serve God, he would have encouraged the people to give their allegiance to "the Lord's anointed" (Rehoboam, grandson of David) instead of making him king. Faithfulness to God was not his chief concern. Those who are already departing the path of righteousness often do not consider the consequences for their wrong actions. Such seems to be Jeroboam's case. Consider the prophet who rebuked him as he worshiped at one of those altars he had built.
1 And, behold, there came a man of God out of Judah by the
word of the LORD unto Bethel: and Jeroboam stood by the altar to burn
incense. 2 And he cried against the altar in the word of
the LORD, and said, O altar, altar, thus saith the LORD; Behold, a
child shall be born unto the house of David, Josiah by name; and upon
thee shall he offer the priests of the high places that burn incense
upon thee, and men's bones shall be burnt upon thee. 3 And
he gave a sign the same day, saying, This is the sign which the LORD
hath spoken; Behold, the altar shall be rent, and the ashes that are
upon it shall be poured out. 4 And it came to pass, when
king Jeroboam heard the saying of the man of God, which had cried
against the altar in Bethel, that he put forth his hand from the
altar, saying, Lay hold on him. And his hand, which he put forth
against him, dried up, so that he could not pull it in again to him.
5 The altar also was rent, and the ashes poured out from
the altar, according to the sign which the man of God had given by the
word of the LORD. 6 And the king answered and said unto the
man of God, Entreat now the face of the LORD thy God, and pray for me,
that my hand may be restored me again. And the man of God besought the
LORD, and the king's hand was restored him again, and became as it was
before. (1 Kings 13:1-6, KJV)
Notice the "thy God" in the king's statement. He does not say "our God" or "my God." It is almost as if Jeroboam admits to not having the same God.
Conclusion
Jeroboam's making of the golden calves was part of a bigger picture of establishing his throne and maintaining his authority over the tribes who had already shown their willingness to rebel against their rightful king. He was not prompted by a desire to serve the true God, but for self-aggrandizement.