We do not believe in animal sacrifices. These were "additions" to the Torah. No blood can atone for sins whether it is human or animal blood. Animals can however be offered to God for "thanks" giving purposes or for worship. Animal sacrifices cannot remove sin so no amount of sacrificing them will make atonement.
We learn from the book of Jeremiah that God did not authorise animal sacrifices.
For I spoke not unto your fathers, nor commanded them on the day that I brought them out of the land of Egypt, concerning burnt-offerings or sacrifices; but this thing I commanded them, saying, "Obey my voice, and I will be your God, and ye shall be my people; and walk ye in all the ways that I have commanded you, that it may be well unto you.
"The multitude of your sacrifices-- what are they to me?" says the LORD. "I have more than enough of burnt offerings, of rams and the fat of fattened animals; I have no pleasure in the blood of bulls and lambs and goats.
This is a clear corruption in the Torah. The Jews added animal sacrifices into the Torah. But we learn from the beginning God did not authorise these things. The blood of animals will not atone sins. Pliny believes the Essenes rejected the animal sacrificial system whilst others suggest they stayed away from the Temple because they rejected the authorities in power. Ebonite's likewise believed animal sacrifices were a corruption of the Torah and believed they should be eliminated. The Nazarenes also rejected sacrifices:
"Nazarenes, which rejected the Pentateuch, regarding it as a forgery; they observed most Jewish customs but did not accept the cult of animal sacrifice (cf. Meyer, Urspr, 2 (1921) (source: http://www.jewishvirtuallibrary.org/jsource/judaica/ejud_0002_0002_0_01153.html)
In any case the scriptures have clear contradictions. On this issue we have determined to reject animal sacrifices as forms of blood atonement.
See this related article: Jesus’ Opposition to Animal Sacrifice (Again)