They provoked him to jealousy - The language is borrowed from the matrimonial relationship, as in Deuteronomy 31:16.

They provoked him to jealousy with strange gods,.... Or "with others" (h); the word "gods" is not in the text, nor were the Jews guilty of worshipping strange gods or idols in the times of Christ, nor had they been from the time of their coming out of the Babylonish captivity; but the word, as Cocceius observes, is used for "another", as in Job 19:27; and signifies other saviours, other messiahs, whom the Jews set up when they rejected Christ, the rock of salvation; and it is observable, that before the coming of Christ, they never attempted to set up any; but, after they had rejected him, were ready to embrace everyone that offered, of which one, called Bar Cochab, the son of a star, in allusion to Numbers 24:17; is a flagrant instance; and whom, when they found themselves deceived, they called Bar Cozba, the son of a lie, or a lying fellow; to whom our Lord may be thought to have respect, John 5:43; and where he expressly calls him another. Now, not only to reject Jesus, the true Messiah, but to set up others in his room, false Christs, was highly provoking to God, who is a jealous God, and will not give his glory to another:

with abominations provoked they him to anger; by advancing the traditions of the elders to an equality with, and above the word of God; and by continuing sacrifices, after the great sacrifice was offered up, when they ought to have ceased; for, by continuing them, it was saying Christ was not come in the flesh, nor his sacrifice offered up; it was trampling under foot the Son of God, and treating his blood and sacrifice with contempt; which must be an abomination to God, and highly provoking of his anger, when that sacrifice was of a sweet smelling savour to him; and especially what was abominable to him, and grievously provoked him to anger and wrath, was their setting up the idol of their own righteousness, refusing to submit to the righteousness of Christ, Romans 10:3; and indeed, whenever anything is set up in competition with him, or in opposition to him, be it what it will, it must be an abomination to God; because it opposes his purposes and resolutions of saving men by Christ alone, reflects on his wisdom in the scheme of salvation, flies in the face of his love, grace, and mercy, makes the death of Christ of none effect, advances pride in the creature, gives God the lie, who says there is no other Saviour, and is a total slight and neglect of his Gospel; all which must be abominable, and dreadfully provoking to him; see Isaiah 65:5;

(h) "per alios", Cocceius.

"They excited His jealousy through strange (gods), they provoked Him by abominations. They sacrificed to devils, which (were) not-God; to gods whom they knew not, to new (ones) that had lately come up, whom your fathers feared not. The rock which begat thee thou forsookest, and hast forgotten the God that bare thee." These three verses are only a further expansion of Deuteronomy 32:15. Forsaking the rock of its salvation, Israel gave itself up to the service of worthless idols. The expression "excite to jealousy" is founded upon the figure of a marriage covenant, under which the relation of the Lord to Israel is represented (vid., Deuteronomy 31:16, and the com. on Exodus 34:15). "This jealousy rests upon the sacred and spiritual marriage tie, by which God had bound the people to Himself" (Calvin). "Strange gods," with which Israel committed adultery, as in Jeremiah 2:25; Jeremiah 3:13. The idols are called "abominations" because Jehovah abhorred them (Deuteronomy 7:25; Deuteronomy 27:15; cf. 2 Kings 23:13). שׁדים signifies demons in Syriac, as it has been rendered by the lxx and Vulgate here; lit., lords, like Baalim. It is also used in Psalm 106:37. - "Not-God," a composite noun, in apposition to Shedim (devils), like the other expressions which follow: "gods whom they knew not," i.e., who had not made themselves known to them as gods by any benefit or blessing (vid., Deuteronomy 11:28); "new (ones), who had come from near," i.e., had but lately risen up and been adopted by the Israelites. "Near," not in a local but in a temporal sense, in contrast to Jehovah, who had manifested and attested Himself as God from of old (Deuteronomy 32:7). שׂער, to shudder, construed here with an accusative, to experience a holy shuddering before a person, to revere with holy awe. - In Deuteronomy 32:18 Moses returns to the thought of Deuteronomy 32:15, for the purpose of expressing it emphatically once more, and paving the way for a transition to the description of the acts of the Lord towards His rebellious nation. To bring out still more prominently the base ingratitude of the people, he represents the creation of Israel by Jehovah, the rock of its salvation, under the figure of generation and birth, in which the paternal and maternal love of the Lord to His people had manifested itself. חולל, to twist round, then applied to the pains of childbirth. The ἁπ. λεγ. תּשׁי is to be traced to שׁיה, and is a pausal form like יחי in Deuteronomy 4:33. שׁיה equals שׁהה, to forget, to neglect.

They provoked him to jealousy with {k} strange gods, with abominations provoked they him to anger.

(k) By changing his service for their superstitions.

32:16 To jealousy - To anger and fury, for jealousy is the rage of a man. And withall it implies the ground of his anger, their falseness to God whom they had accepted as their husband, and their spiritual whoredom with other gods.

32:15-18 Here are two instances of the wickedness of Israel, each was apostacy from God. These people were called Jeshurun, an upright people, so some; a seeing people, so others: but they soon lost the reputation both of their knowledge and of their righteousness. They indulged their appetites, as if they had nothing to do but to make provision for the flesh to fulfil the lusts of it. Those who make a god of themselves, and a god of their bellies, in pride and wantonness, and cannot bear to be told of it, thereby forsake God, and show they esteem him lightly. There is but one way of a sinner's acceptance and sanctification, however different modes of irreligion, or false religion, may show that favourable regard for other ways, which is often miscalled candid. How mad are idolaters, who forsake the Rock of salvation, to run themselves upon the rock of perdition!