Question is straightforward: Why is part of Daniel written in Hebrew but a middle section written in Aramaic?
There are a whole host of explanations that have been proffered. Most of this answer is based on this book which summarises the consensus opinion that the first six chapters and the remaining ones constitute two separate sections (textually that isn't difficult to see, the first section is narrative and the second visionary, they also run chronologically parallel). This of course is almost the basis for an answer to the question - since this dissection is almost in line with the language shift - save the first chapter (which "should" be in Aramaic) and the seventh (which "should" be in Hebrew).
It seems entirely plausible that the first section was composed in Babylon and the second in Israel. This would lend to the explanation that the first chapter's Hebrew is merely introductory (similar to the rest of the more historical accounts of the Bible), while the seventh's Aramaic remains problematic. There is a lovely textual/narrative symmetry that links chapters 2-7 in pairs (2 and 7, 3 and 6, 4 and 5) which would then tie the seventh chapter in some way to the first section, making its Aramaic an understandable choice.
Further opinions speculate simply that the entire book was originally written in Hebrew, but lost, and only the Aramaic translations (which were and still are prevalent because Aramaic was widely spoken) of some sections were preserved. Others speculate precisely the opposite - the entirety was written in Aramaic (being the more universal and diplomatic language of the time) but in order to canonise the book they needed to translate at least some sections to Hebrew. Which chapters to translate could still be explained as above. Still others propose an explanation that is seen in certain parts of Jewish dogma from the same period - that the Aramaic was for the layperson and the Hebrew was for the more academic/elite. This makes a lot of sense in light of the narrative/visionary breakdown.
Another explanation for chapter seven's diversion from the Hebrew of the rest of the section is that it's a connecting link - being contently more like the second section, but in the language of the first.
The simplest explanation is simply redaction. The two languages are a natural result of the bilingual region.
For the last portion of the book there is a frame of sealing. The prophecies were to become relevant for the future after the time in Babylon, when the people would have long settled back in their land and speak their language, Hebrew.
For Daniel Hebrew was not just his mother-tongue, the language of his youth, it was the language of a chosen people. At his old age he still turned towards Jerusalem when he prayed to God. He loved, studied and knew the Law and the Prophets. In his decisions as an official under different kings he had very certainly often relied on Mosaic regulations (which had proven successful to him from young age on).
If he in Babylon in a a foreign environment had retained his Hebrew, those returning to their promised home land could and should regain it, if it should have been lost.
This is the frame of sealed prophecy spanning over the visions of chapers 8 to 12:
'The vision ... that was told to you is correct. But you should seal up the vision, for it refers to a time many days from now.' - Daniel 8:26
'He said, "Go, Daniel. For these matters are closed and sealed until the time of the end.' - 12:29
To write this last part of the book (which really was a collection of documents) in Hebrew would be just natural. With regard to the sealing of these contents it seems more than indicated not to use the Aramaic.
For the first part to be in Hebrew the most likely reason is that there was no written account of these first three years of Daniel's education in Babylon. The beginning of chapter 2 is an introductory link to what was the beginning of Daniel's career as an official of high rank of the Babylonian court. Verses 4b to 11 of chapter 2 (the beginning of the Aramaic text may have been part of a royal protocol and decree (in Aramaic) which followed the reported event.
To continue in Aramaic may (in addition to the fact that the now surrounding and officially used language was Aramaic) be interpreted as Daniel's signal to his fellow countrymen that God's decree for those living in Babylon was to settle and work for the good of the city (which obviously would not mean to shun and despise the language spoken there).
Daniel may have written the first part of the book as an introduction to the collection of documents and accounts he arranged in his old age. The parallelism of the chapters 2 and 7, 3 and 6, 4 and 5 indicates a late arrangement, as well as the end of the first chapter does:
'Now Daniel lived on until the first year of Cyrus the king.' - Daniel 1:21
Please allow me offer an answer that is different than you may have heard, but goes beyond what we can see outwardly and requires faith to see many things together from the "new" and the "old" as one.
Have you noticed the following? In Daniel 2:1, exactly who had the dreams?
It was "Nebuchadnezzar" (and NOT Nebuchadnezzar "the King" or "King Nebuchadnezzar"). We must pay attention to the exact words used in each verse and not assume anything. Each specific Word and verse will be properly fulfilled according to it's exact spiritual time and scripture placement.
Now, look at exactly WHO the Chaldeans respond to.
Do you see exactly WHO they are speaking to (and what they tell him)? They are NOT talking to "Nebuchadnezzar", but to "the King". In God's perfect eyes these are two different "men". One "inner" who is "the King" and one outer who is "Nebuchadnezzar" who is "outer" and appears to be the king according to the flesh (natural outer man).
Now, ponder these verses.
Do you see how in God's eyes we are all two separate people in one body?
God commands us to recognize NO ONE according to their outer natural person or "appearances", but who they truly reveal themselves as from within. This is what is being revealed here in these verses.
"The King" is hidden inside the heart of "Nebuchadnezzar" and these Chaldeans know him and speak HIS language. The same language of Jesus himself.
So, it is my belief that these specific words are a very hidden prophesy that wasn't revealed directly to "Nebuchadnezzar" (the outer man) at that point, but to/through his inner man "The King". They go all the way to Daniel 7:28 and end because that is the true heavenly kingdom of God will finally and fully replace the current Earthly Kingdom of darkness of "Nebuchadnezzar" forever.
This is God himself "piecing together" two entirely different kingdoms (Heavenly and Earthly) written in different spiritual "languages" into one book of prophesy. It is God himself becoming "one" with man.
Here is how you can prove it. It starts in Dan "2""4". These numbers are very important. The "2" is the second Kingdom mentioned and the "4" is the 4th spiritual age. If we go to verse "40", we can see further details of what is "inside" verse "4" and see what occurs from a lower level.
It's the start of the "Kingdom of iron" which is Gods immutable spiritual law". The Kingdoms before this were of Earthly spiritual flesh. This is a divided kingdom of inner spiritual law (God himself speaking Aramaic) and outer "clay" which is a human body.
This is a current regenerated person who has the Lord inside their heart and the Kingdom is the "Medes (inner) and the Persians (outer)". His Kingdom as the "Medes" will rule initially from within us but also from the outside at some point when it becomes "the rock" (Peter) and crushes all the rest until they believe and are reborn too.
The "Persians" are the outer kingdom of the spiritual "flesh" that will be fully circumcised away on/in the "8th spiritual Day", "the day of the Lord". This will fulfill the covenant of Abraham for all humanity and this is occurring right now in the spiritual realms of Earth which are INSIDE US. Each time the Lord reveals a lie we believe about him via his LIVING Word and he speaks his LIVING truth from within, he "circumcises" or cuts away more of the outer fleshly lie (deception) from our minds and hearts. Paul explains this beautifully in Colossians and Romans. This is how a true believer can remain sinless while still in a sinful natural body (outer man). The outer body is merely where all sins are "quarantined" until it is fully removed (circumcised) in death.
This is a true "Jew". One who has been circumcised in their heart or inner man and NOT in the outer man of the flesh. A person with the Lord in their heart has been fully circumcised in their inner man as God placed a "firewall" between the inner and outer man.
God will reveal the most astonishing thing to us one day. Our current bodies that contain sin ARE THE ATONING sacrifice that all the Nation of Earthly Israel is waiting for. It is actually the body of Christ himself, the atoning sacrifice for the sins of the world.
We are in his body right now dying with him. 2 Cor 4:10 Our (outer) body contains sin but is also the atoning sacrifice. This is why according to Mark 15:32 and Matthew 27:42 Christ is STILL dying on the cross. The Greek word "Nun" is in these two verses only. This means right now at this EXACT present time.
See most of the Christian world believes his body was a single natural body. It wasn't. It was a spiritual body that is the container for all mankind, our current outer man's body. His death is a spiritual death but also the natural death of all people too. When he died, we died with him. Rom 6:8, 2 Tim 11, 2 Cor 5:14
His body will fully die and all people are inside it as he is the "last Adam" (Noah) and the body is the "Ark" of the MOST HIGH God's covenant of which he will "pass us through" the flood of the "salting with fire" of Mark 9:49.
That is God's side of the "inner" or spiritual view. Here is man's side.
This "salting" and "purifying" process will continue until all Earthly kingdoms are subdued and God's kingdom is supreme in 7:28-9. All people will be "translated" into the Kingdom of his beloved son. Col 1:13 You can see this play out in Acts of the Apostles as Peter is often the most bold one who will speak the truth to anyone. He is the "edge" of his sword of the spirit who is sent into the toughest spiritual battle - those under heavy spiritual law.
However, the truth is always supreme and will expose all lies and deceptions. It is his very living Word (hidden in the spiritual realms) that each written word points to. His living Word who is Christ his Son will not stop until each letter of the law and written Word is 100% fulfilled.
I am very sorry I wrote so much. I get very excited about the things God is revealing and how he is putting together the entire Bible both old and new into "one new man" - the new creation. Eph 2:14-15