Why wasn't Daniel present when Hanania, Mishael, and Azaria were thrown into the furnace?

Question

In the beginning of the book of Daniel, there is the story of Daniel, Hanania, Mishael, and Azaria's survival on vegetables and water. From this, it is established that they attempted to keep the commandments while living under Babylonian captivity.

Later, there is the story of Nebuchadnezzar forcing his subjects to bow to golden image. From what I understand, the Chaldeans accuse the Jews of ignoring this edit and complain that:

There are certain Jews whom thou hast appointed over the affairs of the province of Babylon, Shadrach, Meshach, and Abed-nego; these men, O king, have not regarded thee: they serve not thy gods, nor worship the golden image which thou hast set up.' (3:12)

Only Hanania, Mishael, and Azaria are named as prominent examples of those who have disobeyed the king and who should be punished. Yet Daniel was accorded much respect after he interpreted Nebuchadnezzar's first dream:

Then the king made Daniel great, and gave him many great gifts, and made him to rule over the whole province of Babylon, and to be chief prefect over all the wise men of Babylon. (2:48-49)

If so, why wasn't Daniel named in the Chaldeans' complaint?

Answer 1

The מצודת (and IIRC the Malbim) answers your question:

"The reason they didn't include Daniel was because the king considered him a god."
^{(Proof: The king bowed down to Daniel at the end of the previous chapter.)}

"How would one expect a god to prostrate himself to an idol?"

ולא הלשינו על דניאל בעבור כי ראו שהמלך חשבו לאלוה ואיך ישתחוה הוא אל הצלם

Answer 2

The Gemara in Sanhedrin said (Sanhedrin 93a)

ודניאל להיכן אזל אמר רב למיכרא נהרא רבא בטבריא ושמואל אמר לאתויי ביזרא דאספסתא ור' יוחנן אמר לאתויי חזירי דאלכסנדריא של מצרים איני והתניא תודוס הרופא אמר אין פרה וחזירה יוצא מאלכסנדריא של מצרים שאין חותכין האם שלה בשביל שלא תלד זוטרי אייתי בלא דעתייהו

The Gemara asks: And where did Daniel go? He certainly did not bow to the graven image, and he was not cast into the furnace. Apparently, he was elsewhere. Rav says: He went to dig the great river in Tiberias. And Shmuel says: Daniel went to bring choice alfalfa seed from a distance, and therefore he was not in Babylonia. And Rabbi Yoḥanan says: He went to bring the high-quality pigs of Alexandria of Egypt. The Gemara asks: Is that so that he went to bring the pigs? But isn’t it taught in a baraita that Theodosius the doctor says: No cow or sow emerges from Alexandria of Egypt whose womb is not severed so that it will not give birth? The Gemara answers: They were small pigs that he brought without the knowledge of the people of Alexandria.

ת"ר שלשה היו באותה עצה הקב"ה ודניאל ונבוכדנצר הקב"ה אמר ניזיל דניאל מהכא דלא לימרו בזכותיה איתנצל

The Sages taught: Three were partners in that plan to ensure that Daniel would not be in Babylonia when the decree of persecution was in effect: The Holy One, Blessed be He; Daniel; and Nebuchadnezzar. The Holy One, Blessed be He, said: Let Daniel go from here, so that people would not say that Hananiah, Mishael, and Azariah were delivered from the fiery furnace due to the virtue of Daniel, rather than due to their own righteousness.

ודניאל אמר איזיל מהכא דלא ליקיים בי (דברים ז, כה) פסילי אלהיהם תשרפון באש

And Daniel said to himself: I will go away from here so that this verse will not be fulfilled in my regard: “The graven images of their gods shall you burn with fire” (Deuteronomy 7:25). Daniel was concerned that because Nebuchadnezzar worshipped him like a deity, his legal status was that of an idol, and he would be burned

ונבוכדנצר אמר יזיל דניאל מהכא דלא לימרו קלייה לאלהיה בנורא ומניין דסגיד ליה דכתיב (דניאל ב, מו) באדין מלכא נבוכדנצר נפל על אנפוהי ולדניאל סגיד וגו':

And Nebuchadnezzar said: Daniel should go away from here so that the people will not say: Nebuchadnezzar burned his god in fire. And from where is it derived that Nebuchadnezzar worshipped Daniel? It is derived from a verse, as it is written: “Then the king Nebuchadnezzar fell upon his face and worshipped Daniel and commanded that they should offer an offering and pleasing aromas to him” (Daniel 2:46).

Answer 3

Malbim says it slightly differently: Nevuchadnetzar can't practically have ALL THE PEOPLE bow to the statue, so he's asked the leaders of each city, tribe, nation, etc. to bow, as representatives of the entire population. At this point, Chananya, Mishael, and Azarya are governors or councilmen or whatever similar position that has them included; Daniel is an advisor to the king, but is not in charge of any particular group. (Think more like the White House Chief of Staff.) Thus, no symbolism in him bowing.