Daniel 11:31 — And arms shall stand on his part, and they shall pollute the sanctuary of strength, and shall take away the daily sacrifice, and they shall place the abomination that maketh desolate.
Antiochus IV Epiphanes of the Seleucids profaned the Temple in 167 BC. Daniel 11:31 certainly applies to Antiochus. The disciples understood what Jesus was referring to when he spoke of “the abomination of desolation” due to the prior fulfillment of the Daniel 11:31 prophecy by Antiochus.
I agree with John Calvin in his Commentary on Daniel.
The angel here joins together Antiochus and these impious apostates (cf. 2 Maccabees 5:2). To favor him, the temple is said to be polluted, and this was fulfilled when the statue of Jupiter Olympius was erected there. The tyranny and violence of Antiochus continued long afterwards, as we shall see in its own place. He brought the statue of the Olympian Jove into the temple, for the purpose of overthrowing the worship of God, and then he introduced other corruptions, which vitiated the purity of God’s service. He might in one moment have overthrown the whole Law, but he first tried to mingle many superstitions with God’s Law, and thus to estrange the Jews by degrees from true and sincere piety. The angel speaks of the sanctuary of power, to shew the faithful that Antiochus is not the conqueror of God, who was never deprived of his power, but continued the guardian and keeper of his temple even unto the end. He uses this epithet for the temple, to assure the pious that God had not given way to the violence of the tyrant. His authority stood untouched and untainted, although his temple was exposed to such foul pollution (Calvin in his Commentary on Daniel 11:31).
Daniel 11:31 refers to the desecration of the Temple by Antiochus IV Epiphanes in 167 BC. This cannot refer to the desecration of the Temple in AD 70. I discuss this interpretation more fully in the sections, “Historical Background and Resources: Old Testament References and Allusions – Judas Maccabeus” and “Daniel’s Third Kingdom – Judas Maccabeus.”