Are the passages from Daniel 9:27, 12:7-10, and Matthew 24:15-21 not describing the same "abominable" force of "desolation"?
The word "abomination" is used three times in the book of Daniel (Dan 9:27 (plural), 11:31 and 12:11). The Hebrew word is 8251 in Strong's Exhaustive Concordance:
from 8262; disgusting, i.e. filthy; especially idolatrous or (concretely) an idol; abominable filth (idol, -ation), detestable (thing).
For 8262 it says:
a primitive root; to be filthy, i.e. (intensively) to loathe, to pollute:- abhor, make abominable, have in abomination, detest, * utterly.
The word is used in the singular in 1 Kings 11:5, 11:7 (twice), 2 Kings 23:13 (three times).
From these texts it can be seen that an "abomination" is not a force but rather a disgusting idol, or detestable false god.
So where an abomination is said to "stand in the holy place" it is most likely a statue/idol representing a false god or an alter or shrine to a false god (Matt 24:15), standing either in the Jerusalem Temple or on the holy site of the Jerusalem Temple, where the Temple had once stood.
As others have already said, an alter was built to Zeus in the Temple in Jerusalem by Antiochus IV Epiphanes: this lead to rebellion by the Jews against the Seleucids and this rebellion lead to Jewish independence under the Hasmonians/Maccabees, a "golden age" of Jewish independence. The action of Antiochus Epiphanes accounts for the mention of "abomination of desolation" in Daniel 11:31.
When our Lord speaks of the abomination in Matthew 24:15 he must either be speaking of Dan 12:11 or Dan 9:27. In that Daniel 11:31 is referring to exactly the same false god, i.e. Zeus/Jupiter, you could say verse Daniel 11:31 is also being referred to. In other words, what happened in the days of Antiochus Epiphanes with an abomination to Zeus will happen again: only the name will be the Latin name for Zeus, i.e. Jupiter.
The use in Dan 12:11 seems to be figurative, the main purpose of this section being an encouragement to patience and perseverance in times of trouble. The 1290 days is about three and a half years, a time often used in Scripture to represent a time of chastening and suffering (James 5:17; Rev 11:2, 12:6, 13:5, 12:14).
The most likely verse Matthew 24:15 refers directly to, is Daniel 9:27.
Matthew 24 is a difficult passage because it is our Lord's reply to two entirely different questions 1. When will the Temple be destroyed? and 2. When will be the end of the age? (Matt 24:1-3). These two events were closely associated together in the minds of the disciples. It seems they thought the Temple would survive until "the end of the age".
Q: Why did our Lord not immediately correct this mistake? A: Because he would not have them believe there is a vast gap between the destruction of the Temple and the end of the age. Q. And why would he not want them to believe that? A. Because not even He, in his human nature, knew if it were true or false (Mark 13:32). Q. So why not tell them there might be a big gap between the time of the Temple's destruction and the end of the age? A. Because he wants them and us to be always spiritually awake and ready for the end of the age; for the Son of Man shall come as a thief in the night.
I cannot deny that the following interpretation of Matthew 24 has problems, but I think interpreting the abomination of desolation to have appeared at the time of the Temple destruction (AD 70) has much greater problems.. there was no abomination at that time, and there was no desolation either. The following interpretation has both. Though the destruction of the Temple in AD 70 was bad, something far worse happened during the Kokhba Rebellion ending AD 135. The mere destruction of the Temple in AD 70 was something from which the Jews could recover. It had happened in the past and they had recovered from it. The destruction that happened in the Bar Kokhba Rebellion ending AD 135 was something from which the Jews could not possibly recover... ever. The Bar Kokhba Rebellion was the final chapter of a 2000 year era for the Jewish people.
In Matthew 24, our Lord takes the opportunity to speak of future things in general. One thing must be remembered: our Lord did not know the day of his return to judge the world (Mark 13:32). In his divine nature he knew, but in his human nature he did not know.
He tells them what he does know: the Temple will be destroyed, the abomination of desolation will come, many will rise up claiming to be the Christ, etc. Having finished talking in general about future things he returns to answering their original question (of verse 3): in v34-36 he talks of "these things" and of "that day and that hour". The "these things" in v34 refers back to the destruction of the Temple, and that alone.
On this understanding, the "abomination of desolation" (verse 15) is not related to the destruction of the Temple (AD 70). It is mentioned in the passage speaking generally of future things. The truth is there is nothing of any historical consequence that happened at the time of the Temple destruction that can be spoken of as the abomination of desolation.
However, in the days of the Emperor Hadrian about AD 130 a Temple to Jupiter was set up on the Temple mount, the site where the Jewish Temple had been. (" Jupiter" is the Latin name for Greek god "Zeus".) This lead to the 3rd Jewish Roman War, the Bar Kokhba Rebellion. The Jews remembered and were greatly encouraged to think how successful they had been the last time an idol was set up at the Temple in the days of Antiochus Epiphanes about 168 BC. It had lead to nearly a 100 years of Jewish independence. They believed Emperor Hadrian's idol was an afront to the honour of God. They believed God would be with them as they sought to throw off the Roman rule. They believed the hour had come for the Kingdom of God which they believed was a physical, earthly kingdom in which the Jews were the masters. They believed the man who was promising to lead them to military success. They thought he was their long-promised Messiah.
Simon Bar Kokhba had changed his name. Really "Bar Kokhba" was a title, his father's not was not "Kokhba". Bar Kokhba, "Son of the Star", is a reference to Numbers 24:17. Many Jews, not just in Palestine but in the diaspora, who had rejected Jesus as the Messiah believed Simon Bar Kokhba to be the Messiah: afer all, they had been expecting him to come, the general timing in the book of Daniel pointing to the time of his coming being very close, or even his coming was overdue.
At one time it is said about 400,000 Jewish men were involved in the rebellion, it gained independence for three years. When the Romans finally regained control they were extremely brutal against the Jews, Jerusalem was flattened, and many towns and villages destroyed. Some call the vengeance a time not far short of genocide; we are told about half a million Jews were sold into slavery.
But what was truly devastating for the Jews was the destruction of the their genealogical records showing their descent from Abraham, Isaac and Jacob. Without these records there was no coming back for the Jews as the covenant people of God: that covenant was based on genealogical descent from Abraham. Without the records no Jew could prove they had access to the privileges of the Abrahamic Covenant: the Covenant came to an end. It can never be reinstated. There is no coming back for the Jews.
The abomination of desolation in Matthew 24 is the Temple to Jupiter set up in the days of Hadrian. The Jews had faith in Simon Bar Kokhba thus demonstrating they had no faith in Jesus of Nazareth and no love for God. They rather hated Jesus (without a cause) and suffered the consequences.
The Jews had rejected utterly that they were sinners needing a spiritual Messiah. They believed they were good enough for God, even the only ones in the world who were. Proud self-righteousness undid them. They thought the Law of Moses required only an outward show of obedience: they neither loved the laws of God truly in their hearts nor the One who had given them. If we are the same as them we must expect the same judgement.
The real cause for the destruction of the Jews in the Bar Kokhba rebellion was their rejection of Jesus our Lord, revealed by their faith in another.