Why were Shadrach, Meshach and Abed-nego thrown into a fiery furnace?
Daniel's friends disobey King Nebuchadnezzar
"Therefore at that time certain Chaldeans came forward and accused the Jews. They spoke and said to King Nebuchadnezzar, "O king, live forever! You, O king, have made a decree that everyone who hears the sound of the horn, flute, harp, lyre, and psaltery, in symphony with all kinds of music, shall fall down and worship the gold image; and whoever does not fall down and worship shall be cast into the midst of a burning fiery furnace. There are certain Jews whom you have set over the affairs of the province of Babylon: Shadrach, Meshach, and Abed-Nego; these men, O king, have not paid due regard to you. They do not serve your gods or worship the gold image which you have set up.
Then Nebuchadnezzar, in rage and fury, gave the command to bring Shadrach, Meshach, and Abed-Nego. So they brought these men before the king. Nebuchadnezzar spoke, saying to them, "Is it true, Shadrach, Meshach, and Abed-Nego, that you do not serve my gods or worship the gold image which I have set up? Now if you are ready at the time you hear the sound of the horn, flute, harp, lyre, and psaltery, in symphony with all kinds of music, and you fall down and worship the image which I have made, good! But if you do not worship, you shall be cast immediately into the midst of a burning fiery furnace. And who is the god who will deliver you from my hands?"
Shadrach, Meshach, and Abed-Nego answered and said to the king, "O Nebuchadnezzar, we have no need to answer you in this matter. If that is the case, our God whom we serve is able to deliver us from the burning fiery furnace, and He will deliver us from your hand, O king. But if not, let it be known to you, O king, that we do not serve your gods, nor will we worship the gold image which you have set up (Daniel 3:8-18).
Everyone worshipped the image of the king except for Shadrach, Meshach and Abed-nego. The Babylonian priests brought this situation to the attention of Nebuchadnezzar and accused the men of not worshipping the gods of the Chaldeans and not worshipping the image of the king. Nebuchadnezzar became extremely angry and ordered the men be brought before him. He demanded that they worship his image and they refused. They told him that they would never serve his gods or worship his image. They said they would trust God to deliver them from the furnace.
It is possible that the Chaldean priests enticed Nebuchadnezzar into building the golden image of himself and demanding that everyone worship it because they knew the Hebrews would not worship the image and hoped the king would have them out to death. Their first and main target was Daniel, but when the image was ready for worship Daniel was not in Babylon. It seems he was out of Iraq or even the empire on the king's business of some sort. This first attempt to have Daniel and his companions killed failed as but they tried again many years later.