Hebrews 10:3

But in those sacrifices there is a remembrance made of sins year by year. For it is impossible that the blood of bulls and goats should take away sins.

Concerning the manner in which there was a remembrance of sins each year, and the same sins at that, see under preceding verse. Behold the contrast between the old law and the new, in the matter of their most sacred ceremonies and sacrifices on the Day of Atonement, which were directed to the remembrance of sins for which daily, weekly, monthly and seasonal sacrifices had already been offered. On the other hand, look at the contrast in the new covenant where the glorious function of the solemn observance of the Lord's Supper is not to call to mind the sins of the worshipers but to remember Christ, his death, his truly efficacious atonement, and his love for the redeemed. Remember sins; remember Christ! What a difference! Any intrusion upon the mind of the worshiper with regard to the remembrance of sins is swallowed up by the thought of that glorious sacrifice in Christ by which sins are removed forever and remembered no more. As Jeremiah spoke of it, "For I will be merciful to their iniquities, and their sins will I remember no more" (Jeremiah 31:31ff). Thus, the New Testament worshiper comes into divine service not to recall his sins but to remember the Lord who said, "This do in remembrance of me."

For it is impossible, ... Common sense alone is the proof of the statement that the blood of animals cannot take away sin, but it is reaffirmed by the word of inspiration. On account of God's having commanded animal sacrifices, there was always the danger that men would assume some value as pertinent to them; hence, the prophets repeatedly instructed Israel to the contrary. As Macknight noted,

Micah formerly taught the Jews the same doctrine and even insinuated to them that the heathens, being sensible of the impossibility of making atonement for sins by shedding the blood of beasts, had recourse to human sacrifices, in the imagination that they were more meritorious (Micah 6:7).[6]

Not the least of the reasons why animal sacrifices could be of no avail lies in the fact that animals never belonged to man in the first place. "For every beast of the forest is mine, and the cattle upon a thousand hills, saith the Lord" (Psalms 50:10). It was thus manifestly erroneous for man to think that by sacrificing some of his fellow creatures of a lower order than himself, and which like himself were the property of God, he could make any true expiation for his sins.