2 Kings 2:23-24 is a fascinating and in some ways worrisome passage, especially as it is represented in many translations of the Bible. There is a more reasonable explanation for the violent event than simply removing things from their context and imagining that Elisha simple used a couple bears to kill some children who were mocking him.
It's important to note that at this point in history, the northern kingdom of Israel has taken upon itself the identity of Canaan.
Centuries earlier, Joshua had led the people of Israel out of the wilderness, over the Jordan, and into the land of Canaan at God's mandate. Israel was simultaneously reaping the promise of blessing with which God had privileged them and acting as the arm of God's divine judgment against a people who had set themselves up as the enemies of God. As God judges all men, so he here judged the civilizations residing in the land of Canaan (doing so in the earthly realm as a pedagogical tool for future generations) and Joshua acts as his divinely appointed hand. The inhabitants of Canaan perished because they had positioned themselves as the enemies of God.
A few hundred years after Joshua's conquer of Canaan, the kingdom of Israel split into two separate nations, the Southern Kingdom of Judah (which comprised Jerusalem and the temple—where ordained worship of God occurred) and the Northern Kingdom of Israel. As the Northern Kingdom had no ordained center of worship, its newly founded king, Jeroboam, decided to create two—rather than risk Israelites heading into the Southern Kingdom in order to worship and falling under Judah's power. To counter Judah's prominence as the center of worship, Jeroboam set up altars in both Bethel and Dan.
And yet here he begins to reverse Joshua's accomplishment by inviting the Northern Kingdom to taking on the identity of Canaanites rather than as the people of God. In Dan and in Bethel, Jeroboam crafts golden calves, intentionally reminiscent of that prepared by Aaron on Sinai, and invokes Sinai's peculiar Aaronic benediction saying, "You have gone up to Jerusalem long enough. Behold your gods, O Israel, who brought you up out of the land of Egypt" (1 Kings 12:25ff). Jeroboam invites the Northern Kingdom to forego worship of God in Jerusalem and sets precedent for them to worship crafted gods, as the Canaanites had.
A couple more centuries pass and the Northern Kingdom has fully embraced its identity as being a nation who will have nothing to do with the God who had brought them to the land they inhabit. They have, for all intents, become the enemies of God every bit as much as the Canaanites had been before them. It is into this land and before this people that the story of Elisha insinuates itself.
Elisha, like Joshua before him, is operating as the hand of God on earth. He renders judgment and offers mercy as God does. And it is in this capacity as God's servant that he comes to Bethel, one of the centers of pagan worship and headquarters of the enemies of God. And out of the city come the servants of the temple, the officials and leaders of idolatrous worship, to call down curses on Elisha and to threaten his life. These are the self-proclaimed enemies of God and they threaten the life of God's own envoy and servant. It is little wonder they meet with a bad end.
But how are we to know that these are servants of the temple? Most translations describe them as children or young men.
The word Hebrew translated here as "children" (na'ar) often means official or servant and doesn't necessarily even refer to age at all. Mephibosheth's servant Ziba is referred to as na'ar (2 Samuel 16:1), yet he has fifteen sons. The man that Boaz has positioned as boss over his fieldworkers is na'ar—not a position one grants to children (Ruth 2:5-6). The word na'ar is translated as "servant" over fifty times (roughly a fifth of the times it appears in Scripture).
Not only were these men servants of pagan deities, they heard of Elisha's approach and came to meet him with threats. It had been big and recent news that Elisha's mentor Elijah had just vanished from the face of the earth. While Scripture records that he had been taken up to heaven alive and in a chariot of flame, many at the time believed that this was merely a cute story to cover up Elijah's death. In saying "Go on up!" They are both mocking what they presume to have been the death of Elijah and a threatening similar fate (death) to Elisha.
These truly are the enemies of God and Elisha. They have willingly taken on the identity of those who Joshua, God's divine hand, was commanded to conquer. They have chosen to be conquered by their choice to oppose the army of the Lord. And so, it seems less drastic then that Elisha should pass judgment on those who, as enemies of God, are threatening the life of the earthly hand of God.