From Hebrews 9 (emphasis added):
11 But when Christ came as high priest of the good things that have come to be, passing through the greater and more perfect tabernacle not made by hands, that is, not belonging to this creation,
12 he entered once for all into the sanctuary, not with the blood of goats and calves but with his own blood, thus obtaining eternal redemption.
13 For if the blood of goats and bulls and the sprinkling of a heifer’s ashes can sanctify those who are defiled so that their flesh is cleansed,
14 how much more will the blood of Christ, who through the eternal spirit offered himself unblemished to God, cleanse our consciences from dead works to worship the living God.
Christ’s one perfect sacrifice permanently did away with the need for anyone to offer animal sacrifice. For a Christian to continue to offer animal sacrifice seems, to me, to be a denial of the efficacy of Christ’s sacrifice.
And yes, I agree that it is wrong to make animals suffer needlessly.