It is the abomination of desolation. The man of sin erects an image in the temple, and demands to be worshiped as God. Your premise is faulty, on purpose.
You need to stop thinking in strict english categories until you have the picture. But I don't know how a person like you ever gets the picture when you screw history.
There is a predicted rebellion in 8:13, with a leader, and it is going to ruin Israel. The expression starts as that, the rebellion that desolates Israel and a rebellion is an abomination. (Remember, for all the separation of the Torah, the unusual thing about Daniel was the command he received to 'seek the prosperity of the city where you have been place.' That is a hint of what was to come.) We have to see the dismay of Daniel in his wait for the prayer to be answered. How could Israel possibly be desolated? And what is even more strange, how could it be desolated while Messiah succeeds in what he was going to do?
The vision of ch 9 is necessarily connected. That rebellion has a timestamp. The guy leading it will ruin the place, though admittedly how a 3rd party is involved with the rebel leader is not clear. The end of the rebellion is in that generation, considered a flood to the end, which is why the flood imagery of Mt 25 exists. Messiah accomplishes the Gospel, while the charming rebel leader ruins Israel.
the history could not be more clear. It is exactly what happened.
If you feel compelled to make something about ch 11-12 change that picture, I don't know how you change history.
The blame of the 8-9 scenario falls on Israel for following a rebel, hence it is a rebellion that (causing) desolation. It does not fall on Israel for a 3rd party bringing in a pagan image. Christ didn't do that either. He said the person, the AofD, would be found in the temple and also be rounding up people in the wilderness. Every other Israelite would follow him. We know from Christ's own experience that claiming to be God at the temple was the height of irreverence, and that person would do so, claiming to have God's power to be victorious against Rome as in Israel's past battles.
It is all dialed in to that generation of Israel, which is why the 'test' of that generation is such a strong theme in Hebrews. And the end of the world was expected shortly.
With the clarity of that picture and of Christ about that picture, I see no need to be concerned about 11-12's material, for which I think there are reasons it applies to other intertestament battles.
It is totally puzzling to me, when there are skeptics who want to move everything in Daniel to the intertestament period (both origination and subject), that such a clear segment of 8-9 is missed equally by skeptics as by D'ists.
It must be that appeal you have, STP, 'just believe me.' You move everything to the future, which as far as I know has not happened yet, and say 'just believe.' That's what irrationality is. They are irrationally against God announcing the future; you are irrationally against history where that announcement was fulfilled.