Animal sacrifice is probably repulsive to modern day people because we love animals so much. I just watched a TV show on "Animal Planet" where incredible rescues were made of all sorts of animals. Much time, money, energy, etc. was put into saving these animals -- both pets and wild animals. But, because they are living creatures, we do what we can to protect them. I think in some respects it stems from our "city" rather than farming upbringing -- but even on farms -- animals are slaughtered for food, etc. -- something which God has allowed.
Really -- the whole problem with animal sacrifice is that a perfect, innocent animal would have to die because of OUR sin -- nothing that the animimal had done. Sadly, very often for us (as it was for them -- see Jer. 7:21-26) our hearts become hard, and we forget that innocent blood was shed on our behalf.
The punishment we deserve fell on Someone else -- an innocent Lamb. Perhaps we would sin a little less -- or take it much less lightly if we could truly picture ourselves placing our hands upon the head of Jesus, then slaying Him, each time we sin.