The book of Leviticus discusses many of the sacrifices performed by the Levitical priests. In some places, it seems to claim that a particular offering could remove sins.
And he shall do with the bull as he did with the bull as a sin offering; thus he shall do with it. So the priest shall make atonement for them, and it shall be forgiven them. (Leviticus 4:20)
Yet the book of Hebrews explicitly states that animal blood could not take away sins.
For it is not possible that the blood of bulls and goats could take away sins. (Hebrews 10:4)
This is fairly simple to resolve. Nowhere in the Old Testament is it ever claimed that sins were “taken away” (i.e., completely removed) by animal sacrifices. The root of the Hebrew word translated “atonement” in the Old Testament is kaphar, which has the idea of “covering,” not total removal. This word is also used to refer to how Noah’s ark was to be covered with pitch.
Make yourself an ark of gopherwood; make rooms in the ark, and cover it inside and outside with pitch. (Genesis 6:14, emphasis added)
Tens of thousands of animals were ceremonially slaughtered by Jewish priests for centuries, the spilling of their blood vividly illustrated the deadly seriousness of sin. However, these sacrifices were essentially like a bandage, only acting as a covering for sin. They did not, and could not, remove sin, as Hebrews 10:4 clearly states.
By that will we have been sanctified through the offering of the body of Jesus Christ once for all. And every priest stands ministering daily and offering repeatedly the same sacrifices, which can never take away sins. But this Man, after He had offered one sacrifice for sins forever, sat down at the right hand of God. (Hebrews 10:10–12)
The phrase “take away” in verse 11 is translated from the Greek root periaireo, which does convey the idea of removal. This is consistent with the use of “atonement” in the Old Testament, as the Levitical sacrifices foreshadowed the final sacrifice of Christ.
Animal sacrifices could only cover sins; they could not remove them. The passage from Hebrews 10 draws a contrast between the animal sacrifices and Christ’s sacrifice. The former could never take away sins, but when Christ shed his own blood, it was a once and for all sacrifice that removes sins.
In this alleged contradiction, the solution is found by simply understanding the context and the proper meanings of the words employed within the text.