Psalm 116:17, Sacrifice of thanksgiving. 

Elsewhere, the psalmist refers to this as “the sacrifice of joy” or praises (Ps 27:6; see also Jer 17:26; 33:11; Heb 13:15), “the sacrifice of righteousness” (Ps 4:5), “the sacrifice of thanksgiving (Ps 107:22), “the freewill offerings of my mouth” (Ps 119:108). Similarly, he declares that the sacrifices of Elohim are  broken spirit and a contrite heart” (Ps 51:17).Paul expresses this concept as “presenting your bodies as a living sacrifice” (Rom 12:1). Why are such sacrifices pleasing to Elohim?

For I desire mercy and not sacrifice, and the knowledge of God more than burnt offerings. (Hos 6:6)

In Matthew 9:13 and 12:7, Yeshua responds to those who were criticizing him for his unconventional religious activities by quoting Hosea 6:6. He goes on to imply that mercy as well as fasting as opposed to literal animal sacrifices is “a new wine skin” for his disciples replacing the old wine skin of animal sacrifices.

Why is the new wine of sacrifice of mercy, praise, righteousness, thanksgiving, a broken spirit and a contrite heart preferable to YHVH-Yeshua over animal sacrifices? The answer should be obvious. One can offer animal sacrifices or perform other religious duties and activities all day long, and never have a heart change. Such means nothing means to Elohim if the sacrifice isn’t accompanies by contrite, repentant, worshipful and thankful heart. Moreover, a sacrifice costs the one giving the sacrifice something, but giving means nothing to Elohim unless it is coupled with a correct heart attitude. Similarly, acts of service are merely a clanging gong and tinkling bell to Elohim if not accompanied by a heart of love (1 Cor 13). YHVH wants hearts that want to love and obey him, not empty acts of religiousity that are done for show and pretense, often out of human pride. Hosea expresses what YHVH wants from humans:

O Israel, return to YHVH your Elohim, For you have stumbled because of your iniquity; take words with you, And return to YHVH. Say to Him, “Take away all iniquity; receive us graciously, for we will offer the sacrifices of our lips. Assyria shall not save us, we will not ride on horses, nor will we say anymore to the work of our hands, ‘You are our gods.’” For in You the fatherless finds mercy. I will heal their backsliding, I will love them freely, for My anger has turned away from him. I will be like the dew to Israel; he shall grow like the lily, and lengthen his roots like Lebanon. his branches shall spread; his beauty shall be like an olive tree, and his fragrance like Lebanon. Those who dwell under his shadow shall return; they shall be revived like grain, and grow like a vine. Their scent shall be like the wine of Lebanon. Ephraim shall say, “What have I to do anymore with idols?” I have heard and observed him. I am like a green cypress tree; your fruit is found in Me. Who is wise? Let him understand these things. Who is prudent? Let him know them. For the ways of YHVH are right; the righteous walk in them, but transgressors stumble in them. (Hos 14:1–9)

To Elohim, such a sacrifice that involves the actual heart conversion of the offerer is a “pure offering” and is sweet smelling incense (Mal 1:11; Ps 141:2; Rev 5:8; 8:3), and YHVH will not rebuke his people for such a sacrifice (Ps 50:8).

Yeshua himself set his followers the example of laying down his life by giving himself for us as living sacrifice (Eph 5:2; Heb 9:26), an offering as a sweet smelling aroma to Elohim, even as Paul did in his life and ministry (Phil 2:17). Yeshua’s disciples will follow his and Paul’s example and do the same (1 Cor 11:1; Eph 5:2; Phil 4:18; 1 Pet 2:4).