None of the Old Testament sacrifices actually take away what we would call sin--deliberate disobedience. Notice that the so-called sins are typically more ceremonial in nature, offenses of impurity or otherwise unintentional. You will not find a sacrifice listed for deliberate sins. This is easily observed by scanning Lev. 4:2, 13, 22, 27; 5:15, 18; Numbers 15:22-24, 27-31. These passages explain that it is for UNINTENTIONAL sins that sin offerings, guilt offerings, and burnt offerings are made. In fact, it emphasizes, if anything, that the deliberate sinner is cut off or put to death.
This should not surprise us as Heb. 10:11 says what they already knew, goats and other animals don't ultimately appease for sin. Christ alone does that. Accordingly, the OT sacrifices acts as symbolic gestures of faith on the givers and foreshadows of God's promise to truly satisfy the demands of his justice through some forthcoming means of sacrifice. In other words, to paraphrase a professor of mine, if the "fake" sins demand this much bloodshed and effort, imagine what will be required for the real sins!